Academic Qualification
Ph.D. in Mathematics, Peking University, China, 1984
Master in Mathematics, Peking University, China, 1981
Teaching Area
B.Sc. Courses
"Complex Analysis
Mathematical Analysis III
Mathematical Analysis IV
Mathematical Physics Methods
Functional Analysis
Real Analysis"
M.Sc. Courses
"Mathematics Seminar
Real Analysis
Clifford Analysis
Functional Analysis
Partial Differential Equations
Topics in Partial Differential Equations
Fourier Analysis
Advanced Mathematics"
Introduction to Statistics
Research Area
Harmonic Analysis in Euclidean Spaces
Partial Differential Equations
Complex Analysis of One and Several variables
Clifford Analysis
Time-Frequency Analysis
System Identification
Signal and Image Processing (Edge Detection)
Working Experience
2019 - present Professor, Macau University of Science and Technology
2013 - 2019 Distinguished Professor, University of Macau
2003 - 2012 Full Professor, University of Macau
2005 - 2011 Head of Dept of Math, Full Professor ,University of Macau
2000 - 2002 Associate Professor, University of Macau
1992 - 2000 Senior Lecturer, Lecturer (English system) , University of New England, Australia
1988 - 1992 Research Fellow, Flinders University of South Australia, Australia
1986 - 1988 Research Fellow, Macquarie University, Australia
1984 - 1986 Research Fellow, Institute of Systems Sciences, the Chinese Academy of Sciences
Google Scholar Address
http://scholar.google.co.uk/citations?user=FQ6tQe4AAAAJ&hl=en
Academic Publication
Accepted and Published Refereed Journal papers
(“*” means that the paper is in the latest SCIE, EI, CPCI-S and CJCR (China Journal of Scientific Research) lists. Percentage of the applicants contribution is cited to the end of the item. Before 2000 the authors name order was basically according to the alphabetical way, and after 2000 it was according to variable criteria and requests of the collaborator(s)).
*242[QQLL]Qu W, Qian T, Leong I T, Li P. The sparse representation related with fractional heat equations. Acta Mathematica Scientia, 2024, 44(2): 567-582.
*241[WQ]Wang J, Qian T. Orthogonalization in Clifford Hilbert modules and applications. Banach Journal of Mathematical Analysis, 2024, 18(1): 2.
2023
*240[ZQZQ]Zhang Y, Qu W, Zhang H, et al. Simulation of non-stationary and non-Gaussian stochastic processes by the AFD-Type Sparse Representations. Mechanical Systems and Signal Processing, 2023, 204: 110762.
*239[LQ]Lin C, Qian T. Frequency analysis with multiple kernels and complete dictionary. Applied Mathematics and Computation, 2024, 466: 128477.
*238[YCLT]Yang F, Chen M, Li P, Qu W, Chen J, Qian T. Sparse series solutions of random boundary and initial value problems. International Journal of Wavelets, Multiresolution and Information Processing, 2023: 2350050.
*237[MQ]Mi W, Qian T. A new backward shift algorithm for system identification by a good choice of frequencies. Asian Journal of Control, 2023.
*236[QLQYZ]Chitin Hon, Ieng Tak Leong, Tao Qian, Haibo Yang & Bin Zou. Unconditional Basis Constructed from Parameterised Szegö Kernels in Analytic Hp(D). Complex Analysis and Operator Theory volume 17, Article number: 84 (2023) .
*235[ZLLQ]B Zhu, J Liu, Z Lai, T Qian. Sampling Gaussian stationary random fields: A stochastic realization approach. ISA transactions.
*234[Q2023]T Qian.n-Best kernel approximation in reproducing kernel Hilbert spaces. Applied and Computational Harmonic Analysis.
*233[LYQX]J Li, X Yang, T Qian, Q Xie. The adaptive Fourier decomposition for financial time series. Engineering Analysis with Boundary Elements 150, 139-153
*232[QZLQ]T Qian, Y Zhang, W Liu, W Qu. Adaptive Fourier decomposition‐type sparse representations versus the Karhunen–Loève expansion for decomposing stochastic processes. Mathematical Methods in the Applied Sciences. 2023. 46 (13):14007-14025.
*231[WLQ]HT Wu, IT Leong, T Qian. Weak pre-orthogonal adaptive Fourier decomposition in Bergman spaces of pseudoconvex domains.Complex Variables and Elliptic Equations 68 (4), 568-577.
*230 [MQ]Mai W, Qian T. Algorithm of adaptive Fourier decomposition in H^2(C^+). International Journal of Wavelets, Multiresolution and Information processing 2023.
*229 [HDQ]Huang Y, Deng G T, Qian T. Integral representations in weighted Bergman spaces on tube domains[J]. Complex Variables and Elliptic Equations, 2023: 1-20.
*228 [JLQ]Jin M, Leong I T, Qian T, et al. Adaptive Fourier decomposition of slice regular functions[J]. Advances in Applied Clifford Algebras, 2023, 33(1): 8.
*227[ZMRQJ] Ze, W., Man, W. C., Rosa, A., Tao, Q., & Jung, T. P. (2023). Stimulus-Stimulus Transfer Based on Time-Frequency-Joint Representation in SSVEP-Based BCIs.
2022
*226[DMQ]Dang P, Mai W, Qian T. On Monogenic Reproducing Kernel Hilbert Spaces of the Paley–Wiener Type[J]. Advances in Applied Clifford Algebras, 2022, 32(4): 1-29.
*225[CDQS]Colombo F, De Martino A, Qian T, et al. The Poisson kernel and the Fourier transform of the slice monogenic Cauchy kernels[J]. Journal of Mathematical Analysis and Applications, 2022, 512(1): 126115.
*224[DDQ]Dang P, Du J, Qian T. Riemann Boundary Value Problems for Monogenic Functions on the Hyperplane[J]. Advances in Applied Clifford Algebras, 2022, 32(3): 1-60.
*223[Q2022(2)]Qian T. Positive-instantaneous frequency and approximation[J]. Frontiers of Mathematics in China, 2022, 17(3): 337-371.
*222[FLQ]Fu W Y, Li X D, Qian T. Data-driven ILC algorithms using AFD in frequency domain for unknown linear discrete-time systems[J]. Journal of the Franklin Institute, 2022, 359(6): 2445-2462.
*221[QDZC]Qian T, Dai L, Zhang L, Chen Z. Granular sieving algorithm for selecting best n n parameters[J]. Mathematical Methods in the Applied Sciences, 2022.
*220[LQWZ]Li P, Qian T, Wang Z, Zhang C. Regularity of fractional heat semigroup associated with Schrödinger operators[J]. Fractal and Fractional, 2022, 6(2): 112.
*219[WWRQ]Wang Z, Wong C M, Rosa A, Qian T. Adaptive Fourier Decomposition for Multi-Channel Signal Analysis[J]. IEEE Transactions on Signal Processing, 2022, 70: 903-918.
*218[Q2022]Qian T. Sparse representations of random signals[J]. Mathematical Methods in the Applied Sciences, 2022, 45(8): 4210-4230.
*217[QQLZ] Qu W , Qian T , Haichou Li, Kehe Z,. Best kernel approximation in Bergman spaces[J]. Applied Mathematics and Computation, 2022, 416:126749-.
*216[WLQ] H. T. Wang, I. T. Leong, T. Qian, Adaptive rational approximation in Bergman space on bounded symmetric domain, J. Math. Anal. Appl., 2022, 506(1).
*215[MQ2] W. Mi, T. Qian, System identification of hammerstein models by using backward shift algorithm, Applied Mathematics and Computation, 2022, 413.
*214[MQ1]Mai W, Qian T. The Fourier type expansions on tubes[J]. Complex Variables and Elliptic Equations, 2022, 67(2): 433-461.
*213[LJCQ] D. Li, F. X. Jiang, M. Chen, T. Qian, Multi-step-ahead wind speed forecasting based on a hybrid decomposition method and temporal convolutional networks, Energy, 2022, 238.
2021
*212[QQD]Qu, W., Qian, T., Deng, G., Youfa Li & Chunxu Zhou. Analytic Phase Retrieval Based on Intensity Measurements. Acta Math Sci 41, 2123–2135 (2021).
*211[DQ]Dong B, Qian T. Uniform generalizations of Fueter’s theorem[J]. Annali di Matematica Pura ed
Applicata (1923-), 2021, 200(1): 229-251.
*210[TZQ]Tan C, Zhang L, Qian T, et al. Statistical n-Best AFD-Based Sparse Representation for ECG Biometric Identification[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 1-13.
*209[QCDQ]Qu W, Chui C K, Deng G T, Qian T. Sparse representation of approximation to identity[J]. Analysis and Applications, 2021: 1-23.
*208[WLQ]Wu H T, Leong I T, Qian T. Weak pre-orthogonal adaptive Fourier decomposition in Bergman spaces of pseudoconvex domains[J]. Complex Variables and Elliptic Equations, 2021: 1-10.
*207[WLZQX] Y. F. Wu, X. L. Liu, L. M. Zhang, T. Qian, Q. W. Xie, Content-adaptive image encryption with partial unwinding decomposition, Signal Processing, 2021, 181.
*206[QQH] 钱涛, 曲伟, 黄勇, 算子方程基本问题解的再生核稀疏表示, 中国科学:数学, 2021, 51(01): 209-224.
*205[YQZDB] Z. J. Ye, T. Qian, L. M. Zhang, L. Dai, H. Li, J. A. Benediktsson, Functional Feature Extraction for
Hyperspectral Image Classification With Adaptive Rational Function Approximation, IEEE Transactions on Geoscience and Remote Sensing, 2021, 59.
*204[WQ3] Y. B. Wang, T. Qian, Pseudohyperbolic distance and n-best rational approximation in H2 space, Mathematical Methods in the Applied Sciences, 2021.
*203[DHQ] G. T. Deng, Y. Huang, T. Qian, Reproducing Kernels of Some Weighted Bergman Spaces, Journal of Geometric Analysis, 2021.
*202[TZWQ] C. Y. Tan, L. M. Zhang, H. T. Wu, T. Qian, A novel feature representation approach for single-lead heartbeat classification based on adaptive Fourier decomposition, International Journal of Wavelets, Multiresolution and Information Processing, 2021.
*201[QTC] T. Qian, L. H. Tan, J. C. Chen, A class of iterative greedy algorithms related to Blaschke product, SCIENCE CHINA-MATHEMATICS, 2021.
*200[QWZ] T. Qian, X. Y. Wang, L. M. Zhang, MIMO frequency domain system identification using matrix-valued orthonormal functions, Automatica, 2021, 133.
*199[QQD] W. Qu, T. Qian, G. T. Deng, A stochastic sparse representation: n-best approximation to random signals and computation, Applied and Computational Harmonic Analysis, 2021, 55: 185-198.
*198[XLQL] Q. W. Xie, R. R. Liu, T. Qian, J. Y. Li, Linkages between the international crude oil market and the Chinese stock market: A BEKK-GARCH-AFD approach, Energy Economics, 2021, 102.
2020
*197[CLQ] Q. H. Chen, L. Q. Li, T. Qian, Time-frequency transform involving nonlinear modulation and frequency- varying dilation, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2020, 65(11): 1800-1813 .
*196[DMQ] P. Dang, W. X. Mai, T. Qian, Fourier spectrum of Clifford Hp spaces on R+n+1 for 1 ≤ p ≤ ∞, Journal of Mathematical Analysis and Applications, 2020, 483(1).
*195[YQ] Q. X. Yang, T. Qian, The Dual Elements of Function Sets and Fefferman-Stein Decomposition of Triebel- Lizorkin Functions via Wavelets, COMPUTATIONAL METHODS AND FUNCTION THEORY, 2020, 20(2): 185- 216.
*194[DQ] B. H. Dong, T. Qian, Uniform generalizations of Fueter's theorem, ANNALI DI MATEMATICA PURA ED APPLICATA, 2020, 200(1): 229-251.
*193[CQT] Q. H. Chen, T. Qian, L. H. Tan, A theory on non-constant frequency decompositions and applications, Advancements in Complex Analysis: From Theory to Practice, 2020: 1-37.
*192[FLQ] W. Y. Fu, X. D. Li, T. Qian, AFD-based ILC designs in frequency domain for linear discrete-time systems, INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2020, 51(16): 3393-3407.
*191[CQLX] 陈维国,钱涛,李建平,谢启伟, 基于Takenaka-Malmquist自适应时频分布的特征指标——来自上证和深证的数据, 系统工程理论与实践, 2020, 40(12): 3112-3123.
*190[WQLG] X. Y. Wang, T. Qian, I. T. Leong, Y. Gao, Two-Dimensional Frequency-Domain System Identification, IEEE Transactions on Automatic Control, 65(2): 577-590.
*189[Q2020]T. Qian, Reproducing Kernel Sparse Representations in Relation to Operator Equations. Complex Anal. Oper. Theory, 2020, 14(2): 1–15.
*188[DMQ] P. Dang, W. X. Mai, T. Qian, Fourier spectrum of Clifford Hp spaces on Rn+1+ for 1≤p≤∞, J. Math. Anal. Appl., 2020, 483(1): 123598.
2019
*187[WQLG] X. Y. Wang, T. Qian, I. T. Leong, Y. Gao, Two-Dimensional Frequency-Domain System Identification, IEEE Transactions on Automatic Control, 65(2): 577-590.
*186[Q2020]T. Qian, Reproducing Kernel Sparse Representations in Relation to Operator Equations. Complex Anal. Oper. Theory, 2020, 14(2): 1–15.
*185[DMQ] P. Dang, W. X. Mai, T. Qian, Fourier spectrum of Clifford Hp spaces on Rn+1+ for 1≤p≤∞, J. Math. Anal. Appl., 2020, 483(1): 123598.
*184[CDQ2] Q. H. Chen, P. Dang, T. Qian, Spectra of rational orthonormal systems. Sci. China Math., 2019, 62(10): 1961–1976.
*183[DLQ2] G. T. Deng, H. C. Li, T. Qian, Fourier spectrum characterizations of Hardy spaces Hp on tubes for 0<p<1, Complex Anal. Oper. Theory, 2019, 13(6): 2605–2625.
*182[DHQ] G. T. Deng, Y. Huang, T. Qian, Paley-Wiener-type theorem for analytic functions in tubular domains, J. Math. Anal. Appl., 2019, 480(1): 123367.
*181[MRQZ] W. Mi, H. M. Rao, T. Qian, S. M. Zhong, Identification of discrete Hammerstein systems by using adaptive finite rational orthogonal basis functions, Appl. Math. Comput., 2019, 361: 354–364.
*180[WQ2] Y. B. Wang, T. Qian, Adaptive Fourier decomposition in Hp, Math. Methods Appl. Sci., 2019, 42(6): 2016–2024.
*179[LZQ2] Y. T. Li, T. Qian, A Novel 2D Partial Unwinding Adaptive Fourier Decomposition Method with Application to Frequency Domain System Identification, Mathematical Methods in the Applied Sciences, 2019, 42(9): 3123-3135.
*178[LZQ] Y. T. Li, L. M. Zhang, T. Qian, 2D Partial Unwinding – A Novel Non-Linear Phase Decomposition of Images, IEEE Transactions on Image Processing, 2019, 28(10): 4762-4773.
*177[QWM] T. Qian, J. Z. Wang, W. X. Mai, An Enhancement Algorithm for Cyclic Adaptive Fourier Decomposition, Applied and Computational Harmonic Analysis, 2019, 47(2): 516-525.
*176[DKQS2] B. H. Dong, K. I. Kou, T. Qian, I. Sabadini, The Inverse Fueter Mapping Theorem for Axially Monogenic Functions of Degree k, J. Math. Anal. Appl., 2019, 476 (2): 819–835.
*175[DengLQ] G. T. Deng, H. C. Li, T. Qian, Hardy Space Decompositions of Lp(Rn) for 0<p<1 with Rational Approximation, Complex Var. Elliptic Equ., 2019, 64 (4): 606–630.
2018
*174[MQ5] W. X. Mai, T. Qian, Rational Approximation in Hardy Spaces on Strips, Complex Var. Elliptic Equ., 2018, 63(12): 1721–1738.
*173[QY3] T. Qian, Q.X. Yang, Wavelets and Holomorphic Functions, Complex Analysis and Operator Theory, 2018, 12(6): 1421-1442.
*172[Q20] T. Qian, A Novel Fourier Theory on Non-linear Phases and Applications, ADVANCES IN MATHEMATICS (CHINA), 2018, 47(3): 321-347. (in Chinese).
*171[DMNQ] P. Dang, J. Mourão, J.P. Nunes, T. Qian, Clifford coherent state transforms on spheres, Journal of Geometry and Physics, 2018, 124: 225-232.
*170[GKQ] Y. Gao, M. Ku, T. Qian, Fast algorithm of adaptive Fourier series, Mathematical Methods in the Applied Sciences, 2018, 41(7): 2654-2663.
*169[LDQ2] H.C. Li, G.T. Deng, T. Qian, Fourier Spectrum Characterizations of Hp Spaces on Tubes Over Cones for 1≤p≤∞, Complex Analysis and Operator Theory, 2018, 12(5): 1193-1218.
*168[LQ3] Y.F. Li, T. Qian, Reconstruction of analytic signal in Sobolev space by framelet sampling approximation, Appl. Anal., 2018, 97(2): 94-209.
2017
*167[DLQ] P. Dang, H. Liu, T. Qian, Hilbert Transformation and Representation of the ax+b Group, Canad. Math. Bull., 2017, 61(1): 70-84.
*166[MQ4] W.X. Mai, T. Qian, Aveiro method in reproducing kernel Hilbert spaces under complete dictionary, Mathematical Methods in the Applied Sciences, 2017, 40(18): 1-19.
*165[BDQ] L. Baratchart, P. Dang, T. Qian, Hardy-Hodge Decomposition of Vector Fields in Rn, Transactions of the American Mathematical Society, 2017, 370(3): 2005-2022.
*164[TQ] L.H. Tan, T. Qian, Extracting Outer Function Part from Hardy Space Function, Science China Mathematics, 2017, 60 (11): 2321-2336.
*163[ACQS2] D. Alpay, F. Colombo, T. Qian, and I. Sabadini, Adaptative Decomposition: The Case of the Drury-Arveson Space, Journal of Fourier Analysis and Applications, 2017, 23(6): 1426-1444.
*162[DQC] P. Dang, T. Qian, Q. H. Chen, Uncertainty Principle and Phase–Amplitude Analysis of Signals on the Unit Sphere，Advances in Applied Clifford Algebras, 2017, 27(4): 2985-3013.
*161[GKQW] Y. Gao, M. Ku, T. Qian, J. Z. Wang, FFT formulations of adaptive Fourier decomposition, Journal of Computational and Applied Mathematics, 2017, 324: 204–215.
*160[CDQ] Q. H. Chen, P. Dang, T. Qian, A Frame Theory of Hardy Spaces with the Quaternionic and the Clifford Algebra Settings, Advances in Applied Clifford Algebras, 2017, 27(2): 1073–1101.
*159[KKQ] U. Kähler, M. Ku, T. Qian, Schwarz Problems for Poly-Hardy Space on the Unit Ball, Results in Mathematics, 2017, 71(3-4): 801–823.
*158
[ZKDQ] Y. H. Zhang, K. I. Kou, G. T. Deng, T. Qian,The generalized matsaev theorem on growth of subharmonic functions admitting a lower bound in Rn, Complex Variables and Elliptic Equations, 2017, 62(5): 642–653.
*157[ACQS] D. Alpay, F. Colombo, T. Qian, I. Sabadini, Adaptive orthonormal systems for matrix-valued functions, Proceedings of the American Mathematical Society, 2017, 145(5): 2089–2106.
*156[MNQ] J. Mourão, J. P. Nunes, T. Qian, Coherent State Transforms and the Weyl Equation in Clifford Analysis, Journal of Mathematical Physics, 2017, 58(1): 1-16.
*155[ZQMD] L. M. Zhang, T. Qian, W. X. Mai, P. Dang, Adaptive Fourier decomposition-based Dirac type time-frequency distribution, Mathematical Methods in the Applied Sciences, 2017, 40(8): 2815-2833.
2016
*154[BMQ] L. Baratchart, W.X. Mai, T. Qian, Greedy Algorithms and Rational Approximation in One and Several Variables, In: Bernstein S., Kaehler U., Sabadini I., Sommen F. (eds) Modern Trends in Hypercomplex Analysis. Trends in Mathematics, 2016: 19-33,
*153[DQ] G.T Deng, T. Qian, Rational approximation of Functions in Hardy Spaces, Complex Analysis and Operator Theory, 2016, 10(5): 903-920.
*152[YDQ] Y. Yang , P. Dang, T. Qian, Tighter Uncertainty Principles Based on Quaternion Fourier Transform, Advances in Applied Clifford Algebras, 2016, 26(1): 479-497.
*151[DQY] P. Dang, T. Qian, Y. Yang, Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spacs, Journal of Mathematical Analysis and Applications, 2016, 437(2): 912-940.
*150[LDQ] H. C. Li, G. T.Deng, T. Qian, Hardy space decomposition of on the unit circle: 0<p<1, Complex Variables and Elliptic Equations: An International Journal, 2016, 61(4): 510-523.
*149[QT] T. Qian, L. H. Tan, Backward shift invariant subspaces with applications to band preserving and phase retrieval problems, Mathematical Methods in the Applied Sciences, 2016, 39(6): 1591-1598.
*148[Q] T. Qian, Two-Dimensional Adaptive Fourier Decomposition, Mathematical Methods in the Applied Sciences, 2016, 39(10): 2431-2448.
*147[BCQ] L. Baratchar, S. Chevillard, T. Qian, Minimax principle and lower bounds in H2 rational approximation, Journal of Approximation Theory, 2016, 206: 17-47.
*146[DKQS] B. H. Dong, K. I. Kou, T. Qian, I. Sabadini, On the inversion of Fueter’s theorem, Journal of Geometry and Physics, 2016, 108: 102-116.
*145[ACQS] D. Alpay, F. Colombo,T. Qian, I. Sabadini, The H infinity functional calculus based on the S-spectrum for quaternionic operators and for n-tuples of noncommuting operators, Journal of Functional Analysis, 2016, 271(6):1544-1584.
*144[YQL] Q. X. Yang, T. Qian, P. T. Li, Fefferman-Stein decomposition for Q-spaces and micro-local quantities, Nonlinear Analysis: Theory, Methods &Applications, 2016,145: 24-48.
*143[CQLMZ] Q. H. Chen, T. Qian, Y. Li, W. X. Mai, X. F. Zhang, Adaptive Fourier tester for statistical estimation, Mathematical Methods in the Applied Sciences,2016, 39(12): 3478-3495.
*142[ZDQ] Y. H. Zhang, G. T. Deng, T. Qian, Integral representations of a class of harmonic functions in the half space, Journal of Differential Equations,2016, 260(2): 923-936.
*141[MDZQ] W. X. Mai, P. Dang, L. M. Zhang, T. Qian, Consecutive minimum phase expansion of physically realizable signals with applications, Mathematical Methods in the Applied Sciences,2016, 39(1): 62-72.
*140[MQL] W. Mi, T. Qian, S. Li, Basis pursuit for frequency-domain identification, Mathematical Methods in the Applied Sciences, 2016, 39(3): 498–507.
*139[KMNQ] W. D. Kirwin, J. Mourao, J. P. Nunes, T. Qian, Extending coherent state transforms to Clifford analysis, Journal of Mathematical Physics, 2016, 57(10): 103505.
2015
*138[YDQ] Y. Yang, P. Dang, T. Qian, Stronger uncertainty principles for hypercomplex signals, Complex Variables and Elliptic Equations, 2015, 60(12): 1696-1711.
*137[DDQ] P. Dang, J.Y. Du, T. Qian, Boundary value problems for periodic analytic functions, Boundary value problems, 2015, 143: 1-28.
*136[LQS] X. Lyu, T. Qian, B.-W. Schulze, Order filtrations of the edge algebra, J. Pseudo Differ. Oper. Appl. 2015, 6(3): 279-305.
*135[TQC] L. H. Tan, T. Qian, Q. H. Chen, New aspects of Beurling–Lax shift invariant subspaces, Applied Mathematics and Computation, 2015, 256: 257-266.
*134[CQ] X. D. Chen, T. Qian, Estimation of hyperbolically partial derivatives of of rho-harmonic quasiconformal mappings and its applications, Complex Variables and Elliptic Equations. An International Journal, 2015, 60(6): 875-892.
*133[MoQM] Y. Mo, T. Qian, W. Mi, Sparse Representation in Szegö Kernels through Reproducing Kernel Hilbert Space Theory with Applications, International Journal of Wavelet, Multiresolution and Information Processing, 2015, 13(4): 1550030.
*132[MoQMC] Y. Mo, T. Qian, W. X. Mai, Q. H. Chen, The AFD Methods to Compute Hilbert Transform, Applied Mathematics Letters, 2015, 45: 18-24.
*131[QT] T. Qian, L. H. Tan, Characterizations of Mono-components: the Blaschke and Starlike types, Complex Analysis and Operator Theory, 2015: 1-17, DOI 10.1007/s11785-015-0491-6.
*130[CQS] D. C. Chang, T. Qian, W. Schulze, Corner Boundary Value Problems, Complex Analysis and Operator Theory, 2015, 9(5): 1157-1210.
*129[WjQ] J. X. Wang, T. Qian, Approximation of Functions by Higher Order Szegö Kernels I. Complex Variable Cases, Complex Variables and Elliptic Equations, 2015, 60(6): 733-747.
*128[ChenQTan] Q. H. Chen, T. Qian, L. H. Tan, Constructive Proof of Beurling-Lax Theorem, Chinese Annals ofMathematics, Series B, 2015, 36(1): 141-146.
*127[YDQ] Y. Yang, P. Dang, T. Qian, Space-frequency analysis in higher dimensions and applications, Annali di Matematica Pura ed Applicata, 2015, 194(4): 953-968.
2014
*126[YQL] Q. X. Yang, T. Qian, P. T. Li, Spaces of harmonic functions with boundary values in Q^a_{p,q}, Applicable Analysis, 2014, 93(11): 2498-2518.
*125[SQSW] D. Schepper, T. Qian, F. Sommen, J. X. Wang, Holomorphic Approximation of L_2-functions on the Unit Sphere in R3, Journal of Mathematical Analysis and Applications, 2014, 416(2): 659-671.
*124[Q23] T. Qian, Adaptive Fourier Decomposition, Rational Approximation, Part 1:Theory, International Journal of Wavelets, Multiresolution and Information Processing, 2014, 12(5): 1461008.
*123[ZMHQ] L. M. Zhang, W. X. Mai, W. Hong, T. Qian, Adaptive Fourier Decomposition, Rational Approximation, Part 2: Software System Design and Development, International Journal of Wavelets, Multiresolution and Information Processing, 2014, 12(5): 146100
*122[MoQ1] Y. Mo, T. Qian, Support vector machine adapted Tikhonov regularization method to solve Dirichlet problem, Applied Mathematics and Computation, 2014, 245: 509-519.
*121[XD-Chen-Qian2] X. D. Chen, T. Qian, A sharp lower bound of Burkholder’s functional for K-quasiconformal mappings and its applications, Monatshefte für Mathematik, 2014, 175(2): 195-212.
*120[LLvQ] P. T. Li, J. H. Lv, T. Qian, A Class of Unbounded Fourier Multipliers on the Unit Complex Ball, Abstract and Applied Analysis, 2014, Art. ID 602121, 8 pp.
*119[MQ3] W. Mi, T. Qian, On backward shift algorithm for estimating poles of systems, Automatica, 2014, 50(6): 1603-1610.
*118[QWY] T. Qian, J. X. Wang, Y. Yang, Matching Pursuits among Shifted Cauchy Kernels in Higher-Dimensional Spaces, Acta Mathematica Scientia, 2014, 34(3): 660-672.
*117[QChen] T. Qian, Q. H. Chen, Rational Orthogonal Systems are Schauder Bases, Complex Variables and Elliptic Equations, 2014, 59(6): 841-846.
*116[XD-Chen-Qian] X. D. Chen, T. Qian, Non-stretch mappings for a sharp estimate of the Beurling-Ahlfors operator, Journal of Mathematical Analysis and Applications, 2014, 412(2): 805–815.
*115[LptQt ] P. T. Li, T. Qian, Unbounded holomorphic Fourier multipliers on starlike Lipschitz surfaces and applications to Sobolev spaces, Nonlinear Analysis Series A: Theory, Methods & Applications, 2014, 95: 436–449.
*114[WQ1] J. X. Wang, T. Qian, Approximation of monogenic functions by higher order Szeg\”o kernels on the unit ball and the upper half space, Sciences in China: Mathematics, 2014, 57(9): 1785-1797.
*113[DuQWIII] Z. H. Du, T. Qian, J. X. Wang, Lp polyharmonic Dirichlet problems in regular domains III: The Unit Ball, Complex Variables and Elliptic Equations, 2014, 59(7): 947-965.
*112[Q22] T. Qian, Cyclic AFD Algorithm for Best Rational, Mathematical Methods in the Applied Sciences, 2014, 37(6): 846-859.
*111[LCQW] Y. F. Li, Q. H. Chen, T. Qian, Y. Wang, Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions, Applicable Analysis, 2014, 93(2): 305-315.
2013
*110[LQ2] S. Li, T. Qian, On Sparse Representation of Analytic Signal in Hardy Space, Mathematical Methods in the Applied Sciences, 2013, 36 (17): 2297-2310.
*109[DDQ2] P. Dang, G. T. Deng, T. Qian, A Tighter Uncertainty Principle For Linear Canonical Transform in Terms of Phase Derivative, IEEE Transactions on Signal Processing, 2013, 61(21): 5153 – 5164.
*108[QZ] T. Qian, L. M. Zhang, Mathematical theory of signal analysis vs. Complex analysis method of harmonic analysis, Applied Mathematics-A Journal of Chinese Universities, 2013, 28(4): 505-530.
*107[DuQW] Z. H. Du, T. Qian, J. X. Wang, Lp polyharmonic Dirichlet problems in regular domains IV: The upper-half space, Journal of Differential Equations， 2013, 255(5): 779–795.
*106[LdfQ] D. F. Li , T. Qian, Sufficient conditions that the shift-invariant system is a frame for L2(Rn), Acta Math. Sinica, 2013, 29(8): 1629-1636.
*105[TQ2013] L. H. Tan, T. Qian, Estimations of convergence rate of rational Fourier series and conjugate rational Fourier series and their applications, 中国科学：数学，2013, 43(6): 541-550.
*104[DDQ1] P. Dang, G. T. Deng, T. Qian, A Sharper Uncertainty principle, Journal of Functional Analysis, 2013, 265(10): 2239-2266.
*103[MMQRS] W. X. Mai, Y. Mo, T. Qian, M. D. Riva, S. Saitoh, A Matrix Inequality for the Inversions of the Restrictions of a Positive Definite Hermitian Matrix, Advances in Linear Algebra & Matrix Theory, 2013, 3(4): 55-58.
*102[LQM1] T. Qian, S. Li, W. X. Mai, Sparse Reconstruction of Hardy Signal And Applications to Time-Frequency Distribution, International Journal of Wavelets, Multiresolution and Information Processing, 2013, 11(3): 1350031.
*101[QYQX] T. Qian, Q. X. Yang, Micro-local structure and two kinds of wavelet characterizations about the generalized Hardy spaces, Taiwanese Journal of Mathematics, 2013, 17(3): 1039-1054.
*100[ChenQQLee] Q. H. Chen, T. Qian, Y. F. Li, Shannon-Type Sampling for Non-Bandlimited Signals in Higher Dimensions, Sciences in China, 2013, 56(9): 1915-1934.
*99[LyfQ] Y. F. Li, T. Qian, Analytic sampling approximation by projection operator with application in decomposition of instantaneous frequency, International Journal of Wavelets, Multiresolution and Information Processing, 2013, 11(5): 1350040.
*98[CCQ] M. Chen, X. T. Chen, T. Qian, Quasihyperbolic Distance in Punctured Planes, Complex Analysis and Operator Theory, 2013, 7(3): 655-672.
*97[QWang] T. Qian, Y. B. Wang, Remarks on Adaptive Fourier Decomposition, International Journal of Wavelets, Multiresolution and Information Processing, 2013, 11(1): 1-14.
*96[DQ2] P. Dang, T. Qian, Transient Time-Frequency Distribution based on Mono-component Decompositions, International Journal of Wavelets, Multiresolution and Information Processing, 2013, 11(3): 1350022.
*95[QLS] T. Qian, H. Li, M. Stessins, Comparison of Adaptive Mono-component Decompositions, Nonlinear Analysis: Real World Applications, 2013, 14(2): 1055–1074.
*94[QWe] T. Qian, E. Wegert, Optimal Approximation by Blaschke Forms, Complex Variables and Elliptic Equations, 2013, 58(1): 123-133.
2012
*93[CZQ] L. p. Chen, T. Zhong, T. Qian, Higher Order Boundary Integral Formula and Integro-Differential Equation on Stein Mainfolds, Complex Analysis and Operator Theory, 2012, 6(2): 447-464.
*92[QWj] T. Qian, J. X. Wang, Some Remarks on the Boundary Behaviors of Functions in the Monogenic Hardy Spaces, Advances in Applied Clifford Algebras, 2012, 22(3): 819–826.
*91[MQ] W. Mi, T. Qian, Frequency Domain Identification: An Algorithm Based On Adaptive Rational Orthogonal System, Automatica, 2012, 48(6): 1154-1162.
*90[DQ1] P. Dang, T. Qian, Hardy-Sobolev Derivatives of phase and amplitude and their applications, Mathematical Methods in the Applied Sciences, 2012, 35(17): 2017-2030.
*89[QSW] T. Qian, W. Sproessig, J. X. Wang, Adaptive Fourier decomposition of functions in quaternionic Hardy spaces, Mathematical Methods in the Applied Sciences, 2012, 35(1): 43–64.
*88[YQS2] Y. Yang, T. Qian, F. Sommen, Phase Derivative of Monogenic Signals in Higher Dimensional Spaces, Complex Analysis and Operator Theory, 2012, 6(5): 987-1010.
*87[DQW1] Z. H. Du, T Qian, J. X. Wang, Lp Polyharmonic Dirichlet problems in regular domains, II: The upper half plane, Journal of Differential Equations, 2012, 252(2): 1789-1812.
*86[DeQ] G.T. Deng, T. Qian, An Application of Entire Function Theory to Analytic Signals, Journal of Mathematical Analysis and Applications, 2012, 389(1): 54–57.
*85[MQW] W. Mi, T. Qian, F. Wan, A Fast Adaptive Model Reduction Method Based on Takenaka-Malmquist Systems, Systems & Control Letters, 2012, 61(1): 223–230.
2011
*84[YQ7] Y. Yang, T. Qian, 实系数解析函数的零点集合，Acta Mathematica Sinica, 2011, 31A(5): 1160–1166.
*83[QZL] T. Qian, L. M. Zhang, Z. X. Li, Algorithm of Adaptive Fourier Decomposition , IEEE Transactions on Signal Processing, 2011, 59(2): 5899–5906.
*82[DQ2] P. Dang, T. Qian, Analytic Phase Derivatives, All-Pass Filters and Signals of Minimum Phase, IEEE Transactions on Signal Processing, 2011, 59(10): 4708–4718.
*81[LptLeongQ] P. T. Li , T. Qian, A class of Fourier multipliers on starlike Lipschitz surfaces, Journal of Functional Analysis, 2011, 261(6): 1415-1445.
*80[CQRW] Q. H. Chen, T. Qian, G. B. Ren, Y. Wang, B-Splines of Blaschke Product Type, Computers and Mathematics with Applications, 2011, 62(10): 3669-3681.
*79[YQ6] Y. Yang, T. Qian, Zeroes of Slice Monogenic Functions, Mathematical Methods in the Applied Sciences, 2011, 34(11): 1398–1405.
*78[QTW] T. Qian, L. H. Tan, Y. B. Wang, Adaptive Decomposition by Weighted Inner Functions: A Generalization of Fourier Series, Journal of Fourier Analysis and Applications, 2011, 17(2): 175-190.
*77[QWa1] T. Qian, Y. B. Wang, Adaptive Fourier series—a variation of greedy algorithm, Advances in Computational Mathematics, 2011, 34(3): 279–293.
*76[DQY] P. Dang, T. Qian, Z. You, Hardy-Sobolev spaces decomposition and applications in signal analysis, Journal of Fourier Analysis and Applications, 2011, 17(1): 36–64.
2010
*75[YQ4] Y. Yang, T. Qian, on sets of zeros of clifford-algebra-valued polynomials, Acta Mathematica Scientia, 2010, 30(3): 1004-1012.
*74[ZLQ] D. S. Zhou, D. Z. Liu, T. Qian, Fixed trace $\beta$-Hermite ensembles: asymptotic eigenvalue density and the edge of the ensity, Journal of Mathematical Physics, 2010, 51(3): 033301.
*73[Q21] T. Qian, Intrinsic mono-component decomposition of functions: An advance of Fourier theory, Mathematical Methods in Applied Sciences, 2010, 33(7): 880-891.
*72[QWXZ] T. Qian, R. Wang, Y. S. Xu, H. Z. Zhang, Orthonormal Bases with Nonlinear Phases, Advances in Computational Mathematics, 2010, 33(1): 75-95.
*71[LLQ] H. Li, L.Q. Li, T. Qian, Discrete-Time Analytic Signals and Bedrosian Product Theorems, Digital signal processing, 2010, 20(4): 982–990.
*70[QHLW] T. Qian, I. T. Ho, I. T. Leong, Y. B. Wang, Adaptive decomposition of functions into pieces of non-negative instantaneous frequencies, International Journal of Wavelets, Multiresolution and Information Processing, 2010, 8(5): 813–833.
2009
*69[QWD] T. Qian, Y. B. Wang, P. Dang, Adaptive Decomposition Into Mono-Components, Advances in Adaptive Data Analysis, 2009, 1(4): 703-709.
*68[CQ] Q. H. Chen, T. Qian, Sampling theorem and multi-scale spectrum based on Fourier atom, Applicable Analysis, 2009, 88(6): 903-919.
*67[AKQ] A. Axelsson, K. I. Kou, T. Qian, Hilbert transforms and the Cauchy integral in Euclidean space, Studia Mathematica, 2009, 193(2): 161-187.
*66[GLQ] Y. F Gong, I. T Leong, T. Qian, Two Integral Operators In Clifford Analysis,Journal of Mathematical Analysis and Applications, 2009, 354(2): 435–444.
*65[QY] T. Qian, Y. Yang, Hilbert Transforms on the Sphere With the Clifford Algebra Setting, Journal of Fourier Analysis and Applications, 2009, 15: 753-774.
*64[QXYYY] T. Qian, Y. S. Xu, D. Y. Yan, L. X. Yan, B. Yu, Fourier Spectrum Characterization of Hardy Spaces and Applications, Proceedings of the American Mathematical Society, 2009, 137(3): 971-980.
*63[Q20] T. Qian, Boundary Derivatives of the Phases of Inner and Outer Functions and Applications, Mathematical Methods in the Applied Sciences, 2009, 32: 253-263.
*62[FQ4] M. G. Fei, T. Qian, Pointwise convergence for expansions in spherical monogenics, Acta Mathematica Scientia, 2009, 29B(5): 1241-1250.
*61[FQ3] M. G. Fei, T. Qian, A note on pointwise convergence for expansions in surface harmonics of higher dimensional Euclidean spaces, Taiwanese Journal of Mathematics, 2009, 13(3): 1053-1062.
*60[LPQ1] X. M. Li, L. Z. Peng, T. Qian, The Paley-Wiener Theorem in the non-commutative and non-associative octonions, Science in China Series A: Mathematics, 2009, 52(1): 129-141.
2008
*59[LPQ2] X. M. Li, L. Z. Peng, T. Qian, Cauchy integrals on Lipschitz surfaces in the octonionic space, Journal of Mathematical Analysis and Applications, 2008, 343(2): 763–777.
*58[QZL] T. Qian, L. M. Zhang, H. Li, Mono-components vs. IMFs in signal decomposition, International Journal of Wavelets, Multiresolution and Information Processing, 2008, 6(3): 353-374.
2007
*57[DQ] R. Delanghe, T. Qian, Half Dirichlet problems and decomposition of Poisson kernels, Advances in Applied Clifford Algebras, 2007, 17(3): 383-393.
*56[YQ3] Y. Yang, T. Qian, Co-dimension-p Shannon sampling theorems, Complex Variables and Elliptic Equations, 2007, 52(1): 9-20.
*55[KQS2] K. I. Kou, T. Qian, F. Sommen, Sampling with Bessel functions, Advances in Applied Clifford Algebras, 2007, 17(3): 519-536.
*54[ZQZ] L. M. Zhang, T. Qian, Q. Y. Zeng, Radon measure formulation for edge detection using rotational wavelets, Communication on Pure and Applied Analysis, 2007, 6(3): 899-915.
*53[YQS] Y. Yang, T. Qian, F. Sommen, Codimension-p Paley-Wiener Theorem, Arkiv för Matematik, 2007, 45: 179-196.
2006
*52[FQ2] M. G. Fei, T. Qian, Clifford algebra approach to pointwise convergence of Fourier series on spheres, Sciences of China, 2006, 49(11): 1553-1575.
*51[YQ2] Y. Yang, T. Qian, Schwarz Lemma in Euclidean spaces, Complex Variables and Elliptic Equations, 2006, 51(7): 653-659.
*50[PQS] D. P. Pea, T. Qian, F. Sommen, An alternative proof of Fueter’s theorem, Complex Variables and Elliptic Equations. An International Journal, 2006, 51(8-11): 913–922.
*49[CLQ2] Q. H. Chen, L. Q. Li, T. Qian,Two Families of Analytic Signals with Non-linear Phase, Physica D. Nonlinear Phenomena, 2006, 221(1): 1-12.
*48[FQ1] M. G. Fei, T. Qian, Direct Sum Decomposition of L^2(R^n_1) into Subspaces Invariant Under Fourier Transformation, The Journal of Fourier Analysis and Applications, 2006, 12(2): 145-155.
*47[QC] T. Qian, Q. H. Chen, Characterization of Analytic Phase Signals, Computers & Mathematics with Applications. An International Journal, 2006, 51(9-10): 1471-1482.
*46[YQ1] Y. Yang, T. Qian, An elementary proof of Paley-Wiener Theorem in C^n using Clifford algebra, Complex Variables and Elliptic Equations, 2006, 51(5): 599-609.
*45[Q19] T. Qian, Mono-components for decomposition of signals, Mathematical Methods in the Applied Sciences, 2006, 29(10): 1187-1198.
*44[Q18] T. Qian, Analytic Signals and Harmonic Measures, Journal of Mathematical Analysis and Applications, 2006, 314(2): 526-536.
2005
*43[CLQ1] Q. H. Chen, L. Q. Li and T. Qian, Stability of frames generalized by nonlinear atoms, International Journal of Wavelets, Multiresolutionand Information Processing, 2005, 3(4): 465-476.
*42[Q17] T. Qian, Characterization of boundary values of functions in Hardy spaces with applications in signal analysis, Journal of Integral Equations and Applications, 2005, 17(2): 159-198.
*41[QCL] T. Qian, Q. H. Chen and L.Q. Li, Analytic unit quadrature signals with non-linear phase, Physica D: Nonlinear Phenomena, 2005, 303 (1-2): 80-87.
*40[KQ3] K.I. Kou and T. Qian, Shannon Sampling in the Clifford Analysis Setting, Z. Anal. Anwendungen, 2005, 24(4): 853-870.
*39[KQ2] K.I. Kou and T. Qian, Shannon sampling and estimation of band-limited functions in the several complex variables setting, Acta Mathematica Scientia, 2005, 25(4): 741-754.
2004
38[GQD] Y. F. Gong, T. Qian, J. Y. Du, The structure of solutions of polynomial Dirac equations in Clifford analysis, Complex Variables, 2004, 49(1): 15-24.
2003
*37[QS] T. Qian, F. Sommen, Deriving harmonic functions in higher dimensional spaces, Mathematical Methods in the Applied Sciences, 2003, 22(2): 275-288.
2002
*36[KQS1] K. I. Kou, T. Qian, F. Sommen, Generalizations of Fueter’s Theorem, Methods and Applications of Analysis, 2002, 9(2): 273-289.
*35[KQ1] K. I. Kou, T. Qian, The Paley-Wiener theorem in Rn with the Clifford analysis setting, Journal of Functional Analysis, 2002, 189: 227-241.
*34[Q16] T. Qian, Calderon-type reproducing formulae on Lipschitz curves and surfaces, Journal of the Australian Mathematical Society, 2002, 72: 33-45.
*33[QZ3] T. Qian, T. D. Zhong, Hadamard principal value of higher order singular integrals, Chinese Annals of Mathematics Series A, 2002, 23(2): 205-212.
2001
*32[Q15] T. Qian, Fourier analysis on starlike Lipschitz surfaces, Journal of Functional Analysis, 2001, 183: 370-412.
*31[QY] T. Qian, Q. H. Yu,The schwarzian derivative in Rn, Advances in Applied Clifford Algebras, 2001, 11(S2): 257–268.
*30[QZ2] T. Qian, T. D. Zhong, The differential integral equations on smooth closedorientable manifolds, Acta Mathematica Sinica(Series B), 2001, 21(1): 1-8.
2000
*29[QZ] T. Qian, T. D. Zhong, Transformation formula of higher order singular integrals on the complex hypersphere, Journal of the Australian Mathematical Society (Series A), 2000, 68: 155-164.
*28[JQ] X. H. Ji, T. Qian, Properties of Poisson kernel for a degenerate elliptic equation, Zeitschrift für Analysis and ihre Anwendungen (Mathematical Methods in the Applied Sciences), 2000, 23: 71-80.
1999
27[CQ] M. Cowling, T. Qian, A class of singular integralson the n-complex unit sphere, Scientia Sinica (Series A), 1999, 42(2): 1233-1245.
1998
26[LQ] R. L. Long, T. Qian, Clifford martingale Phi-equivalence between S(f) and f*, Advances in Applied Clifford Algebras, 1998, 8(1): 95-107.
*25[Q14] T. Qian, Singular integrals on star-shaped Lipschitz surfaces in the quaternionicspace, Mathematische Annalen, 1998, 310 (4): 601-630.
1997
24[Q13] T. Qian, Generalization of Fueter’s result to R^{n+1}, Rend. Mat. Acc. Lincei, 1997, 8(9): 111-117.
23[Q12] T. Qian, A holomorphic extension result, Complex Variables, 1997, 32(1): 59-77.
*22[Q11] T. Qian, Singular integrals with holomorphic kernels and Fourier multipliers on star-shape Lipschitz curves, Studia Mathematica, 1997, 123(3): 195-216.
1996
21[GQW] G. Gaudry, T. Qian, S. L. Wang, Boundedness of singular integrals with holomorphic kernels on star-shaped closed Lipschitz curves, Colloquium Mathematicum, 1996, LXX: 133-150.
*20[QR] T. Qian, J. Ryan, Conformal transformations and Hardy spaces arising in Clifford analysis, Journal of Operator Theory, 1996, 35: 349-372.
1994
*19[GQ] G. I. Gaudry, T. Qian, Homogeneous even kernels on surfaces, Mathematische Zeitschrift, 1994, 216: 169-177.
*18[LMQ] C. Li, A. McIntosh, T. Qian, Clifford algebras, Fourier transforms, and singular Convolution operators on Lipschitz surfaces, Revista Matematica Iberoamericana,1994, 10(3): 665-695.
*17[QP] J. Peetre, T. Qian, Möbius covariance of iterated Dirac operators, Journal of the Australian Mathematical Society (Series A), 1994, 56 (3): 1-12.
1993
*16[GLQ] G. I. Gaudry, R. Long, T. Qian, A Martingale proof of L2-boundednessof Clifford-Valued Singular Integrals, Annali di Mathematica Pura Ed Applicata, 1993, 165: 369-394.
1992
*15[GQS] G. Gaudry, T. Qian, P. Sjögren, Singular Integrals related to the Laplacian on the affine group ax+ b, Arkiv for matematik, 1992, 30(2): 259-281.
*14[McQ2] A. McIntosh, T. Qian, Lp Fourier multipliers along Lipschitz curves, Transactions of The American Mathematical Society, 1992, 333(1): 157-176.
1990
13[McQ1] A. McIntosh, T. Qian, A note on singular integralsalong Lipschitz curves with holomorphic kernels, Approximation Theory and its Applications, 1990, 6(4): 40-57.
1989
*12[PQ] L. Z. Peng, T. Qian, A kind of multlinear operators and the Schatten-von Neumann classes, Arkiv for Mat., 1989, 27: 145–154.
1987
11[Q10] T. Qian, BMO boundedness of a certain class of operators, Research and Reviews in Math., 1987, 7(2): 331–332.
1986
*10[Q9] T. Qian, BMO boundedness of maximal operators, Acta Math. Sinica, 1986, 29(3): 317-322.
*9[QL] T. Qian, C. Li, Pointwise estimates for a class of singular integrals and higher commutators, Acta Math. Sinica, new series, 1986, 2(3): 248-259.
8[Q8] T. Qian, Weighted inequalities concerning the Radon measures of the arc-length of curves on the complex plane, Journal of SystemsScience and Mathematical Science, 1986, 6(2): 146-153.
1985
*7[Q7] T. Qian, Commutators of multiplier operators, Chin. Ann. of Math, 1985, 6B (4): 401-408.
6[Q6] T. Qian, Kakeya needle problem, Maths in Practice and Theory, 1985, 3: 64-67.
*5[Q5] T. Qian, Higher Commutators of pseudo-differential operators, Chin. Ann. of Math, 6B(2): 229-240.
4[Q4] T. Qian, Commutators of homogeneous multiplier operators, ScientiaSinica, 1985, XXVIII(3): 225-234.
1984
3[Q3] T. Qian, On estimate for a multilinear singular integral, Scientia Sinica, 1984, XXVIII(11): 1143-1154 .
2[Q2] T. Qian, The preservation of the Lipschitz spaces under several maximal operators, Kexue Tongbao, 1984, 29(4): 443-447.
1983
1[Q1] T. Qian, Lip boundedness of some maximal operators defined on ${\scr H}$-families of sets, Kexue Tongbao (Chinese), 1983,28(21): 1285–1288.
Books and Journal Special Issues Editor
2019
10.Qian, Tao; Li, Pengtao. Singular integrals and Fourier theory on Lipschitz boundaries. Science Press Beijing, Beijing; Springer, Singapore, 2019. xv+306 pp. ISBN: 978-981-13-6499-0; 978-981-13-6500-3 42-02 (42B20 42B25 46E35)
2017
9.New Trends in Analysis and Interdisciplinary Applications, by P. Dang, M. Ku, T. Qian and L. G. Rodino, Trends in Mathematics Research Perspectives.
8.Lipschitz 边界上的奇异积分与 Fourier 理论, by T. Qian and P. T. Li, 科学出版社.
2016
7.Mathematical Analysis, Probability and Applications– Plenary Lectures, by Qian, T. and Rodino, L., Springer Proceedings in Mathematics & Statistics.
2015
6.自适应 Fourier 变换, by Qian, T., 科学出版社.
2012
5.Complex Variables and Elliptic Equations, by T. Qian and Z.H. Du, accepted to appear in 2012.
4.Mathematical Methods in the Applied Sciences, by T. Qian, I.T. Leong, 30 November 2012 Volume 35, Issue 17, Page 1999-2140, Special Issue: Complex Analytic Methods in Signal Processing
2007
3.Communication on Pure and Applied Analysis , by T. Qian and Y. S. Xu (Editors),invited as guest editor for the special issue 6 (3), 2007.
2.Wavelet Analysis and Applications,by T. Qian, V. M. I and Y. S. Xu (Editors), the book series in Applied and Numerical Harmonic Analysis, Springer, 2007.
2004
1.Advances in Analysis and Geometry, by T. Qian, T. Hempfling, A. McIntosh and F. Sommen (Editors) ,book series in Trends in Mathematics, Birkhäuser, 2004.
Book Chapters
2014
"12. [Q24] T. Qian, Fueter mapping theorem in hypercomplex analysis, Springer References: General Aspects of Quaternionic and Clifford Analysis, Operator Theory, edited by Daniel Alpay."
2013
"11. Sparse Representation of Signals in Hardy Space, Quaternionic and Clifford Fourier Transforms and Wavelets, by Eckhard Hitzer and Stephen J. Sangwine, Trends in Mathematics, Birkh\”aser, 2013."
10.[bookchapter10] HOW TO CATCH SMOOTHING PROPERTIES AND ANALYTICITY OF FUNCTIONS BY COMPUTERS, L.P. Castro, H. Fujiwara, T. Qian and Saburou Saitoh, MATHEMATICS WITHOUT BOUNDARIES: SURVEYS IN INTERDISCIPLINARY RESEARCH, Edited by Panos Pardalos and Themistocles M. Rassias, The volume will be published by Springer in 2014.
2008
9.Hilbert Transforms on the Sphere and Lipschitz Surfaces, by T. Qian, Quaternionic and Clifford Analysis, Trends in Mathematics, Birkhäuser Verlag Basel/Switzerland, 259-275, 2008.
2007
8.Mono-components for signal decomposition, book series in Applied and Numerical Harmonic Analysis, Springer, 2007.
7.Time-frequency aspects of nonlinear Fourier atoms, by T. Qian, Q. H. Chen and L. Q. Li, the book series in Applied and Numerical Harmonic Analysis, Springer, 2007.
2004
6.Advances in Analysis and Geometry, by T. Qian, T. Hempfling, A. McIntosh and F. Sommen (Editors), bookseries in Trends in Mathematics, Birkhäuser, 2004.
5.Dini-type convergence of Fourier series on the unit sphere of Euclidean spaces, by T. Qian and S. Liu, book series in Trends in Mathematics, Birkhäuser, 2004, pp131-148.
2001
4.Singular Integrals and Fourier Multipliers On the Unit Spheres and Their Lipschitz Perturbations, Advances in Applied Clifford Algebras, Vol 11, (S1) 53-76, November (2001)– Special Issue, Clifford Analysis Proceedings of the Clifford Analysis Conference, Cetraro, Italy, October, 1998, John Ryan and Daniele C. Struppa Editors.
2000
3.Fourier theory under Möbius transformations, by T. Qian, X. H. Ji, and J. Ryan, CliffordAlgebras and Their Applications in Mathematical Physics, Volume2, edited by John Ryan and Wolfgang Sprössig, Birkhäuser,Boston-Basel-Berlin (April 2000), 51-80.
1995
2.Singular integrals on the m-torus and its Lipschitz perturbations, Clifford Algebras in Analysis and Related Topics, book chapter in the series: Studies in Advanced Mathematics, CRC Press (1995), 94-108.
1991
1.Convolution singular integrals on Lipschitz curves,byT. Qian and A.McIntosh, Springer-Verlag, Lecture Notes in Maths 1494 (1991) 142–162.
Conference Proceedings
2012
16.Sparse Reconstruction of Signals in hardy Spaces, S. Li and T. Qian, the proceedings of QCFTW (of ICCA9) for TIM/Birkhauser, edited by Eckhard MS Hitzer and Steve Sangwine.
2011
15.An adaptive method of model reduction in frequency domain, by Mi Wen and T Qian,IEEE Power Engineering and Automation Conference (PEAM 2011), Sep, Wuhan.
14.Adaptive Fourier Transform Based Signal Denoising, by Zhang, L. M. & Li, H. and Qian, T. (2011). ICSP 2011: International Conference on Signal Processing.
13.Instantaneous Frequencies of Simple Waves and Their application to Sleep Spindle Detection, by Zhang, L.M., Li, H., Wei,Y.T. & Qian, T., Proceedings of 2011 IEEE International Conference on Systems, Man, and Cybernetics (2011).
"12. Non-harmonic system with greedy algorithm, by S. Li and T. Qian, accepted to appear in the International Workshop on Electromagnetism and Communication Engineering”. (ECE 2011), IEEE Catalog Number: CF1143k-DVD, ISBN: 978-1-4244-9438-5, Conference Code: #18262"
2010
11.Frequency Domain Identification with Adaptive Rational Orthogonal System, with M. Wen, Proceedings of 2010 International Conference on System Science and Engineering, Taiwan.
2008
10.A new property of Nevanlinna Functions, by T. Qian, Proceedings of the 16th International Conference of Finite and Infinite Dimensional Complex Analysis and Applications, Dongguk University, Gyeongju, KOREA, July 28-August 1, 2008, pp 38-49.
2003
9.A mathematical model for edge detection using rotational wavelet transformation, by T. Qian andL. M. Zhang, the 6th IASTED International Conference onComputers, Graphics, and Imaging,} August 13-15, 2003, Honolulu,USA.
8.Parameter Analysis of Morlet Wavelet Transform Based Edge Detection, by T. Qian and L. M. Zhang, Proceedings of the 7th WSEASInt. Conf. on CSCC (Circuits, Systems, Communications andComputers)} in Corfu Island, Greece, July 7-10, 2003.
7.Derivation of monogenic functions and applications, Proceedings of the Centre for Mathematics and its applications, Australian University, Volume 41, 2003,118-127.
2002
6.Radon measure formulation of edge detection using rotational wavelets, by T. Qian andL. M. Zhang, Proceedings of the WSEAS conference,Singapore, December, 2002.
5.Paley-Wiener theorem and Shannon Sampling in the Clifford analysis setting, Proceedings of the 6th International Conference on Clifford Algebras and their Applications, Invited Volume for Plenary Talks,May 20-25, 2002, Cookeville, Tennessee, USA.
1996
4.Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space and generalisations to Rn, Proceedings of the Symposium on Analytical and Numerical Methods in Quaternionic and Clifford Analysis, Seiffen, 1996,187-196.
1994
3.Transference between infinite Lipschitz graphs and periodic Lipschitz graphs, Proceedings of the Center for Mathematics and its Applications, ANU, vol.33 (1994), 189-194.
1989
2.A note on martingales with respect to complex measures, by T. Qian, M. Cowling and G. Gaudry, Miniconference onOperators in Analysis (1989), Proceedings of the Center forMathematical Analysis, 24, ANU, Canberra, (1989), 10–27.
1987
1.Fourier transform on Lipschitz curves, by T. Qian and A. McIntosh, Proceedings of the Center for Mathematical Analysis, ANU, vol. 15, (1987), 157–166.
Professional Society Membership
Member of the Australian Mathematical Society
Honorary Positions
Honorary Professor of Huaqiao University since 2011 by invitation
Honorary Professor of Wuhan University since 2005 by invitation
Honorary Professor of Xiamen University since 2003 by invitation
International Journal Editorial Board Positions
Associate Editor: Mathematical Methods in the Applied Sciences (SCI), published by Wiley-Blackwell
Associate Editor: Complex Analysis and Operator Theory (SCI), published by Birkhauser-Springer
Associate Editor: Complex Variables and Elliptic Equations (SCI), published by Birkhauser-Springer
Mathematical Conference Organization
To host ISAAC 2015 in University of Macau
Chair of Scientific and Organization Committees, the 18th International Conference on Finite and Infinite Complex Analysis and Applications, University of Macau, 2010 (120 speakers and two special issues with the SCI journals MMAS and CV&EE as related publications)
Chair of Scientific and Organization Committees, Symposium on Hyper-Complex Analysis, activity of Silver Jubilee of UM, December, 2006 (a conference proceedings published by Univ. of Macau)
Chair of Scientific Committee, the 4th International Conference on Wavelet Analysis and Applications, 29th Nov to 2nd December, 2005, University of Macau (with 150 speakers and a conference book published by Springer)
"Chair of Scientific Committee, Satellite Conference to ICM2002
(International Congress for Mathematicians, 2002, Beijing) on Clifford Analysis and its Applications, August, 2002, University of Macau (a conference book published by Birkhäuser)"
University and Faculty/Unit Service (Position Held, Dates, etc.)
Director of Macau Center for Mathematical Sciences from 2019 to present.
Head of Department of Mathematics for 6 years from 2005 to 2011.
Service as members of University Senate, University GSC and Faculty GSC.
Establishment of a New BSc Program in Mathematics with two branches in University of Macau
Before 2011 Dept of Math taught only service courses for BSc in Math Education of Faculty of Education, and service courses for engineering departments of Faculty of Science and Technology, and Master and Ph.D. programs in mathematics. Supported by the university authority, as Head of Dept of Math, I led colleagues in Dept of Math to establish a new BSc program in mathematics in University of Macau with two streams (Mathematical Education and Mathematics and Applications). The program proposal has passed all the required procedures and become effective since November 2010. In Sep 2011 Dept of Math started to have freshmen for the new BSc in math.
AFD (Adaptive Fourier Decomposition) Algorithm Code Release
Introduction: AFD is a new decomposition model that decomposes a given signal/function into a sum of mono-components (signals of non-negative analytic phase derivative) with fast convergence in energy. Iteration based on AFD gives rise to a conditional solution of the n-best rational approximation: a long standing open algorithm problem.
1. 1D AFD
the agreement to obtain the code of our adaptive Fourier decompositions
2. 2D PUD
the agreement to obtain the code of 2D partial unwinding decompositions
Research Experience
Major Research Grants Obtained From My Working Institutions (Active Research Grants are with thicker color)
2018: Macao Government FDCT 0123/2018/A3, Theory and applications of adaptive fourier decomposition in reproducing Kernel Hilbert spaces.
2018: University of Macau Multi-Year Research Grant (MYRG) MYRG2018-00168-FST, Adaptive rational approximation in weighted Hardy spaces and applications, 1120700 MOP. Funding starts from January 2019.
2017: Macao Government FDCT 079/2016/A2, Studies and Applications of Unwinding Fourier Expansions of Signals. Finding started in January 2018.
2016: University of Macau Multi-Year Research Grant (MYRG) MYRG2016-00053-FST AFD applications in Control Theory, 1458500 MOP.
Annual Research Grant for the position of Distinguished Professor: MOP 350000.
2015: Joined with 乔玉英 NSFC, 11571089, Clifford分析中Dirac型算子及相关问题研究.
2015: Joined with 张艳慧 NSFC, 11501015, 半空间中次调和函数的Matseav定理.
2014: Macao Government FDCT 099/2014/A2, Two Related Topics in Clifford Analysis, Duration: 3 years, MOP 2130000.
2013: Multi-Year Research Grant (MYRG) MYRG116(Y1-L3)-FST13-QT Adaptive Decomposition of Signals and Applications, Level iii project, MOP 120,0000
2013: Multi-Year Research Grant (MYRG) MYRG115(Y1-L4)-FST13-QT Variational Problem on sub-Riemannian geometry with Application in Harmonic analysis and PDE, Level iv research proposal, MOP 221,0000
2012: Macao Government FDCT 098/2012/A3, Approximation With Rational Functions In One and Higher Dimensions With Applications, approved MOP 168, 2850.
2011: Joined with 娄增建，NSFC， 11171203，临界Q型空间及其在流体方程中的应用.
2011: Macao Government FDCT/056/2010/A3, Adaptive Decomposition of Signals and Applications (信号的自适应分解及其应用), Proposed Duration: 3 years. APPROVED MOP 1760000
2009 – 2010: UL017/08-Y3/MAT/QT01/FST, Applications of Hyper-Complex Analysis -1st Sub-project: Signal Analysis. Proposed Duration: 5 years (3rd). Approved 401250 MOP
– 2010: Macao Government FDCT/014/2008/A1, Clifford and Harmonic Analysis Clifford及調和分析Proposed Duration: 3 years. APPROVED MOP$ 1196000
– 2009: UL017/08-Y2/MAT/QT01/FST, Applications of Hyper-Complex Analysis -1st Sub-project: Signal Analysis. Proposed Duration: 5 years (2nd). Approved 195450 MOP
2007: Joined with 娄增建，NSFC， 10771130，Hardy-Sobolev空间及相关问题.
2007 – 2008: RG-UL/07-08S/Y1/QT/FST, Applications of Hyper-Complex Analysis – 1st Sub-project: Signal Analysis. Proposed Duration: Spring of 2008 to End of 2012. Approved 78000 MOP
-2007: RG071/06-07S/QT/FST, Singular Integrals in Hyper-complex Analysis. Proposed Duration: 2 years. Approved 195850 MOP
-2007: RG071/06-07S/08R/QT/FST, Singular Integrals in Hyper-Complex Analysis. Proposed Duration: 2 years. Approved 31000 MOP
2005-2008: Macao Government FDCT/051/2005/A, Time-Frequency Representation and Realization of Algorithm of Transient Signals (瞬變信號的時頻表示及算法實現), Proposed Duration: 3 years. APPROVED MOP$ 500000. Joined by Qiuhui Chen.
2005 -2006: RG059/05-06S/07R/QT/FST, Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis. Proposed Duration: 2 years. Approved 45176.6 MOP
2005 – 2006: RG059/05-06S/08T/QT/FST, Paley-Wiener and Shannon Sampling Theorems in Hyper-Complex Analysis. Proposed Duration: 12 months. Approved 21440 MOP
2004 – 2005: RG059/05-06S/QT/FST (RG079/04-05S), Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis. Proposed Duration: Two year (The present one is the second half). Approved 85580 MOP
2004 – 2005: RG079/04-05S/QT/FST, Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis. Proposed Duration: 24 months. Approved 52170 MOP
2004 – 2005: RG091/04-05S/C117/QT/FST, Clifford Analysis Methods in Harmonic Analysis. Proposed Duration: 2 years. Approved 9487 MOP
2004 – 2005: RG092/04-05S/C118/QT/FST, Analysis Methods in Signal Processing. Proposed Duration: 2 years. Approved 35355.8 MOP
2003 – 2004: RG065/03-04S/QT/FST, Analysis Methods in Signal Processing. Proposed Duration: 2 years. Approved 41700 MOP
2003 – 2004: RG021/03-04S/QT/FST (RG024/02-03S/…), Clifford Analysis Methods in Harmonic Analysis. Proposed Duration: 2 years. Approved 49800 MOP
2002 – 2003: RG024/02-03S/QT/FST, Clifford Analysis Methods in Harmonic Analysis. Proposed Duration: 2 years. Approved 47440 MOP
2002 – 2003: RG080/02-03S/C41/QT/FST (RG055/01-02S…), Mathematical Formulation of Image Edge Detection With Wavelet Method. Proposed Duration: 2 years. Approved 34040 MOP
2001 – 2002: RG055/01-02S/QT/FST (RG002/00-01W.), Monogenic Sinc Function and Applications (Jan to June 2002) & Harmonic Analysis on the Unit Spheres in Higher Dimensional Euclidean Spaces (Jul to Dec2002) Note: Project renewal under the title “Higher Dimensional Sine Methods and Applications in Partial Differential Equations” with a progress report Proposed Duration : one year. Approved 43900 MOP
2001 – 2002: RG056/01-02S/QT/FST, Mathematical Formulation of Image Edge Detection with Wavelet Methods. Proposed Duration: 2 years. Approved 30900 MOP
2001 – 2002: RG056/01-02S/C19/QT/FST, Mathematic Sinc Function and Applications & Harmonic Analysis on the unit Spheres in Higher Dimensional Euclidean Spaces Note: Transfer from 2002 Funding to 2003. Approved MOP$ 26914 MOP
2000 – 2001: RG024/00-01S/QT/FST, Higher Dimensional Sine Methods and Applications in Partial Differential Equations – part 2 (previous ref. RG002/00-01W/QT/FST). Proposed Duration: 1year 3 months (parts 1&2). Approved 39915 MOP
2000 – 2001: RG002/00-01W/QT/FST, Higher Dimensional Sine Methods and Applications in Partial Differential Equations. Proposed Duration: 1 year. Approved 11315 MOP
1993 – 1999 Research Grants obtained yearly from New England University, Australia.
Awards
"澳门特别行政区科学技术奖：自然科学奖一等奖， 二零一二年十月十九日
(Macao SAR Science and Technology Research Award: Natural Science First Prize, the 19th October, 2012)"
Research Prize for Senior Faculty Members, Faculty of Science and Technology, University of Macau, 2007-2009 (The Second Research Competition of University of Macau with only one winner in the category)
2nd Prize of University of Macau Research Award, University of Macau, 2001 (My second year in UM, the first Research Competition of University of Macau)
Vice Chancellor’s Award for Excellency in Research, New England University, Australia, 2000 (One award after several years)
Prize of Scientific Progress, China, 1984, 1985 (joint with M.T. Cheng and D.G. Deng, based on my Doctorate thesis).
