Qian Tao  錢濤
Professor
Head of Department of Mathematics

Academic Qualifications | Working Experience | Teaching | Research | Honorary Positions | Mathematical Conference Organization | Research Grants Recipient | Selected Publications | Professional Affiliations | Contact Details
Academic Qualifications
Working Experience

  • 2000--present 
 Professor, and Head of Dept, University of Macau
  • 1992--2001
 Senior Lecturer, Lecturer (English system)
The 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 Math,
The Chinese Academy of Sciences

Teaching

B.Sc. Courses

  1. Complex Analysis (EDUC302)
  2. Mathematical Analysis III (MATH200)
  3. Mathematical Analysis IV (MATH201)
  4. Mathematical Physics Methods (EDUC414)
  5. Functional Analysis
  6. Real Analysis
M.Sc. Courses
  1. Mathematics Seminar (IMMT102)
  2. Real Analysis (IMAT002)
  3. Clifford Analysis (IMAT005)
  4. Partial Differential Equations (IMAT010)
  5. Topics in Partial Differential Equations (IMMT133)
  6. Fourier Analysis
  7. Advanced Mathematics (IMSE002)
  8. Advanced Mathematics (IMSC001)
Research

Research Interests

Research Grants

  • 2009
 D.A.A.D. the German Research Foundation, Research Stay for Professor two months full living and travel support
  • 2008
 FDCT Macao (119, 6000)
  • 2005
 FDCT Macao (50, 0000)
  • 2000--2006
 University of Macau Research Grants (Every Year)
  • 2006
 Macao Science and Technology Fund
  • 2002
 Grant from Guangdong New Oasis Life Science and Technology Co.,Ltd.
  • 2002
 Conference Grant to the ICM Satellite Conference on Clifford Analysis, Chinese Mathematical Society;
  • 1999--2000
 Cooperating Foundation of Special Fund for Scientific Research, Belgium
  • 1999
 Swedish Foundation for International Cooperation in Research and High Education
  • 1998
 United Nations Development Program
  • 1998
 Joint research project from Chinese Science Foundation
  • 1996
 D.A.A.D. the German Research Foundation

Invited Academic Visiting with Full or Partial Supports

  1. The Center for Mathematical Analysis
    The Australian National University, Australia (1987)
  2. Indiana University, USA (1987)
  3. University of Chicago (1987)
  4. Mittag- Leffler Institute (1992)
  5. University of Stockholm, Sweden (1992)
  6. Chalmers University of Technology, Sweden (1992,1994,1999)
  7. Univ. of Göteborg ,Sweden (1992,1994,1999)
  8. Johannes Kepler University at Linz, Austria (1993)
  9. Delft University of Technology , Netherland (1993)
  10. University of Arkansas, USA (1994)
  11. Washington University at St Louis, USA (1994)
  12. University of Illinois at Urbana-Champaign, USA (1996)
  13. Syracuse University New York, USA (1996)
  14. Banach Center, Poland (invitation, 1996)
  15. Kiel University, Germany (1996, 2007)
  16. Charles University, Prague,Czech Republic (1996, 2007)
  17. Freiberg University, Chemnitz ,Germany (1996, 2007, 2008)
  18. The University of Auckland, New Zealand (1998)
  19. The Univ. of New South Wales, Australia (1998)
  20. Ghent University, Belgium (2001, 2002, 2006)
  21. Aveiro University, Portugal (2003, 2006)
  22. Princeton University, USA (2006)
  23. The University of Alabama, USA (2006)
  24. The Chinese University of Hong Kong, Hong Kong (2001)
  25. Tempare University of Technology, Finland (2006,2007)
  26. University of Helsinki, Finland (2007)
  27. Università degli Studi di Firenze, Italy (2008)
  28. Seminario Matematico e Fisico di Milano, Italy (invitation, 2008)
  29. The Chinese institutions and universities

Plenary Speaker in Conferences

Honorary Positions

Mathematical Conference Organization

Research Grants Recipient

  1. Research grants since 2000 provided by Research Office of University of Macau for various research projects on Clifford analysis, Harmonic Analysis and Signal Analysis;
  2. Research grant provided by FDCT (Macao Government) on signal analysis since 2005 for 3 years;
  3. Chinese Science Foundation joint with Zeng Jian Lou at Shantou University on Hardy-Sobolev Space and Related Subjects, 10771130 (2008-2010).
  4. Chinese Science Foundation joint with Xing Min Li in South China Normal University on Octonions Analysis and Applications (details to be provided)

Selected Publications

Books and Journal Special Issues Editor

  1. Advances in Analysis and Geometry, by Tao Qian, Thomas Hempfling, Alan McIntosh and Frank Sommen (Editors) ,book series in Trends in Mathematics, Birkhäuser, 2004.
  2. Wavelet Analysis and Applications, T. Qian, V.M. I and Y-S. Xu (Editors), the book series in Applied and Numerical Harmonic Analysis, Springer, 2007.
  3. Communication on Pure and Applied Analysis , by T. Qian, Y-S. Xu (Editors) ,invited as guest editor for the special issue Vol 6, No. 3 (Sept, 2007).

Book Chapters

  1. Convolution singular integrals on Lipschitz curves,by T. Qian, AlanMcIntosh, Springer-Verlag, Lecture Notes in Maths 1494 (1991) 142--162.
  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.
  3. Fourier theory under Möbius transformations, by T. Qian and X.H. Ji, 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.
  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.
  5. Dini-type convergence of Fourier series on the unit sphere of Euclidean spaces, by T. Qian and Liu Shuang, book series in Trends in Mathematics, Birkhäuser, 2004, pp131-148.
  6. Advances in Analysis and Geometry, by Tao Qian, Thomas Hempfling, Alan McIntosh and Frank Sommen (Editors), bookseries in Trends in Mathematics, Birkhäuser, 2004.
  7. Time-frequency aspects of nonlinear Fourier atoms, by Tao Qian, Qiu-hui Chen and Luo-qing Li, the book series in Applied and Numerical Harmonic Analysis, Springer, 2007  (Editors: T. Qian, V.M. I and Y-S. Xu).
  8. Mono-components for signal decomposition, book series in Applied and Numerical Harmonic Analysis, Springer, 2007 (Editors: T. Qian, V.M. I and Y-S. Xu ).
  9. Hilbert Transforms on the Sphere and Lipschitz Surfaces, by Tao Qian, Quaternionic and Clifford Analysis, Trends in Mathematics, 259-275, © 2008 Birkhäuser Verlag Basel/Switzerland.

Conference Proceedings

  1. Fourier transform on Lipschitz curves, with Alan McIntosh, Proceedings of the Center for Mathematical Analysis, ANU, vol. 15, (1987), 157--166.
  2. A note on martingales with respect to complex measures, with Michael Cowling and Garth Gaudry, Miniconference onOperators in Analysis (1989), Proceedings of the Center forMathematical Analysis, 24,  ANU, Canberra, (1989), 10--27.
  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.
  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.
  5. Derivation of monogenic functions and applications, Proceedings of the Centre for Mathematics and its applications, Australian University, Volume 41, 2003,118-127.
  6. 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.
  7. Radon measure formulation of edge detection using rotational wavelets, withLiming Zhang, Proceedings of the WSEAS conference,Singapore, December, 2002.
  8. Parameter Analysis of Morlet Wavelet Transform Based Edge Detection, with Liming Zhang , Proceedings of the 7th WSEASInt. Conf. on CSCC (Circuits, Systems, Communications andComputers)} in Corfu Island, Greece, July 7-10, 2003.
  9. A mathematical model for edge detection using rotational wavelet transformation, withLiming Zhang, the 6th IASTED International Conference onComputers, Graphics, and Imaging,} August 13-15, 2003, Honolulu,USA.

Journal papers (Being marked with "*" means that the paper is in the latest SCI list. Being in blue means that the pdf file of the paper will shown when double click the mouse pointing at the paper)

1. The preservation of the Lipschitz spaces under several maximal operators, Kexue Tongbao, vol. 29, no.4, April (1984), 443—447.
2. On estimate for a multilinear singular  integral, Scientia Sinica, vol. XXVII, no.11, Nov. (1984), 1143--1154 .
3. Commutators of homogeneous multiplier operators, ScientiaSinica, vol. XXVIII no.3, March (1985), 225—234.
*4. Higher Commutators of pseudo-differential operators, Chin. Ann. of Math,6B(2) (1985), 229—240.
5. Kakeya needle problem, Maths in Practice and Theory, no. 3 (1985), 64—67.
*6. Commutators of multiplier operators, Chin. Ann. of Math, 6B(4) (1985), 401—408.
7. Weighted inequalities concerning the Radon measures of the arc-length of curves on the complex plane, Journal of SystemsScience and Mathematical Science, vol.  6 no.2, (1986), 146—153.
*8. Pointwise estimates for a class of singular integrals and higher commutators, by Tao Qian and Li Chun, Acta Math. Sinica, new series (1986), Vol. 2 no.3, 248—259.
*9. BMO boundedness of maximal operators, Acta Math. Sinica, vol. 29 no.3, (1986), 317—322.
10. BMO boundedness of a certain class of operators, Research and Reviews in Math., vol.7 no.2, May (1987), 331--332.
11. A kind of multilinear operators and the Schatten-von Neumannclasses, by Tao Qian and Peng Lizhong, Arkiv for Mat. 27, (1989), 145--154.
12. A note on singular integrals with holomorphic kernels,by Tao Qian and Alan McIntosh, Approximation Theory and its Applications, No. 4,vol. 6 (1990) 40--57.
*13. Lp Fourier multipliers along Lipschitz curves, by Tao Qian and Alan McIntosh, Transactions of The American Mathematical Society,Volume 333, Number 1, September (1992), 157--176.
*14. Singular Integrals related to the Laplacian on the affine group ax+b, 1, by T.Qian, G.Gaudry and Peter Sjögren, Arkiv for matematik, Vol. 30 (1992) No 2, 259--281.
*15. A Martingale proof of L2-boundedness of Clifford-Valued Singular Integrals, by T.Qian, G. I. Gaudry and R. Long,Annali di Mathematica Pura Ed Applicata, vol. 165 (1993), 369-394.
*16. Möbius covariance of iterated Dirac operators, by Tao Qian and JaakPeetre, J. Austral Math. Soc. (Series A) 56 (1994), 1-12.
*17. Clifford algebras, Fourier transforms, and singularConvolution operators on Lipschitz surfaces, by Tao Qian, C. Li and A. McIntosh,Revista Matematica Iberoamericana, 10 No.3 (1994), 665-695.
*18. Homogeneous even kernels on surfaces, by Tao Qian and G.I. Gaudry,Mathematische Zeitschrift  216 (1994), 169-177.
*19. Conformal transformations and Hardy spaces arising in Clifford analysis, by T. Qian and J. Ryan, Journal of Operator Theory, 35 1996, 349-372.
20. Boundedness of singular integrals with holomorphic kernels on star-shaped closed Lipschitz curves, by T. Qian,G. Gaudry and S.L. Wang, Colloq. Math, Vol.LXX (1996),133-150.
*21. Singular integrals with holomorphic kernels and Fourier multipliers on star-shape Lipschitz curves, Studia Mathematica, 123(3) (1997),195-216.
22. A holomorphic extension result, Complex Variables, vol 32(1)(1997), 59-77.
23. Generalization of Fueter's result to R^{n+1}, Rend. Mat. Acc. Lincei, s.9, v.8 (1997) 111-117.
*24. Singular integrals associated with holomorphic functional calculus of the spherical Dirac operator on star-shaped Lipschitz surfaces in the quaternionic space, Mathematische Annalen, 310 (4) (April, 1998),601-630.
*25. Poisson kernel of a degenerate elliptic equation,by T. Qian and X.H. Ji, Zeitschrift für Analysis and ihre Anwendungen (Mathematical Methods in the Applied Sciences),Vol. 23 (2000), pp 71-80.
26. Clifford martingale Phi-equivalence between S(f) and f* , by R-L. Long and T. Qian,Advances inApplied Clifford Algebras 8 No.1, 95-107 (1998).
27. A class of singular integrals on the n-complex unit sphere, by T. Qian and M. Cowling,Scientia Sinica (Series A), vol 42, No.12 (December 1999), 1233-1245.
*28. Transformation formula of higher order singular integrals on the complex hypersphere, by T.Qian and T.D. Zhong, Austral Math. Soc.,vol. 68, Part 2 (April 2000), 152-164.
*29. The differential integral equations on smooth closed orientable manifolds, by Tao Qian and T.D. Zhong, Acta Mathematica Sinica, 2001, vol 21, Series B, No.1, 1-8.
*30. Fourier analysis on starlike Lipschitz surfaces, Journal of FunctionalAnalysis, 183, 370-412 (2001).
*31. Hadamard principal value of higher order singular integrals, by T. Qian and T-D. Zhong, The Chinese Annals ofMathematics, 23 A: 2 (2002), 205-212.
*32. Calderon-type reproducing formulae on Lipschitz curves and surfaces, J. Austral. Math. Soc.  72 (2002),33-45.
*33. The Paley-Wiener theorem in Rn with the Clifford analysis setting, by K.I. Kou and T. Qian, Journal of Functional Analysis, 189 227-241 (2002).
34. Generalizations of Fueter's Theorem, by T. Qian, K.I.Kou and F. Sommen, Method and   Applications of Analysis, Vol. 9, No.2, pp. 273-290, June 2002.
*35. Deriving harmonic functions in higher dimensional spaces, by T. Qian and F. Sommen, Zeitschrift für Analysis and ihre Anwendungen (Mathematical Methods in the Applied Sciences), Vol 22 (2003)2, 275-288.
36. The structure of solutions of polynomial Dirac equations in Clifford analysis, by Y-F. Gong, T. Qian and J-Y. Du, Complex Variables, vol. 49, No. 1, pp. 15-24, 15 January2004.
*37. Shannon sampling and estimation of band-limited functions in the several complex variables setting, by K.I.Kou and T. Qian, Acta Mathematica Scientia, 25(4), 2005, 741-754.
*38. Shannon Sampling in the Clifford Analysis Setting, by K.I.Kou and T. Qian, J. Math Anal. Appl., 24 No. 4, 825-842, (2005).
*39. Analytic unit quadrature signals with non-linear phase, by T. Qian, Qiu-hui Chen and Lou-qing Li, Physica D: Nonlinear Phenomena, Pages 80-87. 303 (2005), 80-87.
*40. Analytic Signals and Harmonic Measures, J. Math. Anal. Appl. 314 (2006) 526-536.
41. Characterization of boundary values of functions in Hardy spaces with applications in signal analysis, Journal of Integral Equations and Applications, Volume 17, Number 2, Summer 2005, pp 159-198.
*42. Stability of frames generalized by nonlinearatoms, by Qiu-hui Chen, Luo-qing Li and Tao Qian, International Journal of Wavelets, Multiresolutionand Information Processing, Vol. 3, No. 4 (December 2005) 465-476.
*43. Mono-components for decomposition of signals, Mathematical Methods in the Applied Sciences (Zeitschrift für Analysis and ihre Anwendungen), 2006; 29:1187-1198.
44. An elementary proof of Paley-Wiener Theorem in C^n using Clifford algebra, byYan Yang and Tao Qian, Complex Variables and Elliptic Equations, volume 51, number 5-6, 599-609.
*45. Characterization of Analytic Phase Signals, by Tao Qian and Qiu-hui Chen, Computers & Mathematics with Applications, Vol. 51, 1471-1482, 2006.
*46. Direct Sum Decomposition of L^2(R^n_1) into Subspaces Invariant Under Fourier Transformation, by Ming-gang Fei and Tao Qian, The Journal of Fourier Analysis and Applications, Volume 12, Issue 2, 2006, 145-155.
47. A generalization of Fueter’s theorem, by Dixan Pena Pena, T. Qian and Frank Sommen, Complex Variables and Elliptic Equations, Vol. 51, Nos. 8-11, August-November 2006, 913-922.
*48. Two families of analytic signals with non-linear phase, by Qiu-hui Chen, Luo-qing Li and Tao Qian, Physica-D: Non-linear Phenomena, Vol. 221, 1-12, 2006.
49. Schwarz Lemma in Euclidean spaces, by Yan Yang and Tao Qian, Complex Variables and Elliptic Equations, Vol. 51, No.7, July, 2006, 653-659.
*50. Co-dimension-p Paley-Wiener Theorem, by YanYang, Tao Qian and Frank Sommen, Ark. Mat., 45 (2007) 179-196.
*51. Radon measure formulation for edge detection using rotational wavelets, by Liming Zhang, Tao Qianand Qingye Zeng, Communication on Pure and Applied Analysis , Vol 6, No. 3 (Sept, 2007). 899-915.
*52. Clifford algebra approach to pointwise convergence of Fourier series on spheres, by Ming-gang Fei and Tao Qian, Sciences of China, 49(11), 2006, 1553-1575.
53. Sampling in Bessel functions, by K.I. Kou, T. Qian and Frank Sommen, Advances in applied Clifford Algebra, 17(3), 2007, 519-536.
54. Co-dimension-p Shannon sampling theorems, by Yan Yang and Tao Qian, Complex Variables and Elliptic Equations, 52(1), 2007, 9-20.
*55. A note on pointwise convergence for expansions in surface harmonics of higher dimensional Euclidean spaces, by Ming-gang Fei and Tao Qian, accepted to appear in Taiwanese Journal of Mathematics June Issue of 2009.
*56. Pointwise convergence for expansions in spherical monigenics, by Ming-gang Fei and Tao Qian, accepted to appear in Acta Mathematica Scientia.
*57. Mono-components vs. IMFs in signal decomposition, by Tao Qian, Li-ming Zhang and Hong Li, International Journal of Wavelets, Multiresolution and Information Processing. Vol. 6, No. 3 (May 2008), 353-374.
58. Half Dirichlet problems and decomposition of Posson kernels, by R. Delanghe and Tao Qian, 17 (2007), 383-393, Advances in Applied Clifford Algebra.
*59. The Paley-Wiener Theorem in the non-commutative and non-associative octonions, by X.M. Li, L.Z. Peng and T. Qian, 中国科学  A辑  第38卷 第6期, (2008) (English version has also appeared).
*60. Cauchy integrals on Lipschitz surfaces in the octonionic space, by X.M. Li, L.Z. Peng and T. Qian, Math. Anal. Appl. 343(2008), 763-777.
*61. Boundary Derivatives of the Phases of Inner and Outer Functions and Applications, Mathematical Methods in the Applied Sciences (Math. Meth. Appl. Sci., or Zeitschrift für Analysis and ihre Anwendungen) 2009; 32:253-263.
*62. Fourier Spectrum Characterization of Hardy Spaces and Applications, by T. Qian, Y-S. Xu, D-Y. Yan, L-X. Yan and B. Yu, accepted to appear in Proceedings of the American Mathematical Society.
*63. Hilbert Transforms on the Sphere With the Clifford Algebra Setting, by T. Qian and Y. Yang, accepted to appear in Journal of Fourier Analysis and Applications.
*64. Two Integral Operators In Clifford Analysis, by Y-F Gong, I-T Leong and T. Qian, accepted to appear in Journal of Mathematical Analysis and Applications.
*65. Orthonormal Bases with Nonlinear Phases, by T. Qian,R. Wang, Y-S. Xu and H-Z. Zhang, accepted to appear in Advances in Computational Mathematics (AiCM ).
*66. Hilbert transforms and the Cauchy integral in Euclidean space, by A. Axelsson, K.I. Kou and T. Qian, accepted to appear in Studia Mathematica.
*67. Q. H. Chen and T. Qian, Sampling theorem and multi-scale spectrum based on Fourier atom, accepted by Applicable Analysis.
*68. P. Dang, T. Qian and Z. You, Hardy-Sobolev spaces decomposition and applications in signal analysis, accepted by Journal of Fourier Analysis and Applications.
*69. T. Qian, I.T. Ho, I.T. Leong, Y.B. Wang, Adaptive decomposition of functions into pieces of non-negative instantaneous frequencies, accepted by International Journal of Wavelets, Multiresolution and Information Processing.
*70. Y. Yang and T. Qian, On sets of zeroes of Clifford algebra-valued polynomials, accepted by Acta Math Sinica.
*71. T. Qian, Intrinsic mono-component decomposition of functions: An advance of Fourier theory, accepted by Mathematical Methods in Applied Sciences.
*72. T Qian, Y-B. Wang and P. Dang, Adaptive Decomposition Into Mono-Components, Advances in Adaptive Data Analysis, special issue.

Submitted Journal Papers with Available pdf Files

  1. T. Qian, L-H. Tan and Y-B. Wang, Adaptive Decomposition by Weighted Inner Functions: A Generalization of Fourier Series.
  2. T. Qian and Y-B. Wang, Adaptive Decomposition Into Basic Signals of Non-negative Instantaneous Frequencies - A Variation and Realization of Greedy Algorithm.
  3. Y. Yang and T. Qian, On Sets of Zeroes of Clifford Algebra-Valued Polynomials.
  4. Y, Yang and T. Qian, Zero-sets of Clifford Analytic Functions with Real Coefficients.

Professional Affiliations
Contact Details

Faculty of Science and Technology
University of Macau
Av. Padre Tomás Pereira, Taipa,
Macau, China

Room: N504
Telephone: (853) 8397-4954
Fax: (853) 28838314
Email: fsttq