主题：(更新)Wavelets for Different Dilation Matrices

报告题目：Wavelets for Different Dilation Matrices（小波方面）

报告人：Keith Frederick TAYLOR（加拿大达尔豪西大学副校长）

时间：2009.3.3（周二）下午3点半

地点：理科楼207

内容提要: In the theory of multi-dimensional wavelets, a particular
dilation matrix is fixed. We will explore the connections between the
nature of the dilation matrix and the nature of the possible wavelets
admitted by that matrix.

 

CURRICULUM VITAE

• Academic Credentials:

o    B.Sc., St. Francis Xavier, 1971, Honours Mathematics.

o    Ph.D., University of Alberta, 1976, Mathematics.

• Employment History:

o    Post-doctoral Fellow (NRC PDF), Boulder, Colorado, 1/1/1976 to 30/6/1977.

o    Assistant Professor, 1/7/1977, Department of Mathematics, University of Saskatchewan (U of S).

o    Associate Professor, U of S, 1/7/1981.

o    Full Professor, U of S, 1/7/1987.

o    Full Professor, Department of Mathematics & Statistics, Dalhousie University, 1/8/2003-present.

o    Short-term visiting appointments: Dalhousie (83-84), Paderborn (various), Singapore (10/98-11/98).

• Honours:

o    University of Saskatchewan Master Teacher Award, May Convocation, 2001.

o    University of Saskatchewan Student Union Teaching Excellence Award, 1996-97.

o    U of S 1997 Web'wards - President's Educational Site Award for the MRC web course.

• Primary Research Interests: (See Appendix 1)

o    Abstract Harmonic Analysis and Wavelet Analysis

o    Spectral Problems Arising in Chemistry

o    Technology Enhanced Pedagogy

• Graduate Students: (See Appendix 2)

o    Supervised five PhD theses

o    Supervised nine MSc theses

• Administrative Contributions:

o    Associate Vice-President Academic Outreach and International Programs, 1/8/2008-present.

o    Dean, Faculty of Science, Dalhousie University, 2003-2008.

o    Acting Dean, College of Arts & Science, U of S, 2002-2003.

o    Associate Dean (Science), U of S, 2001-2006 appointment. Served 2001-2002.

o    Vice-President (Western) of the Canadian Mathematical Society (CMS) (1999-2001)

o    Founding director of the Math Readiness Summer Camps (1996-present).

Research Interests

My main scientific research areas are abstract harmonic analysis, wavelet analysis and spectral problems arising in chemistry.

Abstract Harmonic Analysis: This theory is a common generalization of the theory of the Fourier Transform and the Representation Theory of Finite Groups. The theory is generally concerned with analysis on locally compact groups which usually arise as the symmetries of some physical situation. Hence there is a rich interplay between abstract harmonic analysis and areas of physics and chemistry. My abstract work has mainly concentrated on the structure of mathematical objects (irreducble representations, dual spaces, operator algebras) that are constructed to help us analyze the groups of interest. I have had a long standing research collaboration with Prof. E. Kaniuth, University of Paderborn, Germany in this area. This collaboration has been funded by two NATO Collaborative Research Grants, the German Research Foundation and my NSERC grant.
Wavelet Analysis: Around 1985, a new approach to analyzing, storing, denoising, and compressing signals and images emerged. Since then, both the theory and applications of wavelet analysis have developed rapidly with a tremendous impact on almost every area of science, engineering and medicine that involves the manipulation of signals or images. As an example, the FBI collection of fingerprints are now compressed, stored and recovered, as necessary, with a wavelet based algorithm. It turned out that my knowledge in abstract harmonic analysis had an immediate application to the fundamental theory of wavelets. Spectral Problems Arising in Chemistry: Large matrices with a special structure can be associated with families of hydrocarbon molecules and similar matrices can be associated with certain chemical reaction systems. Kenichi Fukui initiated a research project to study problems connected to the spectra of these matrices. His student, Shigeru Arimoto, joined our Mathematical Chemistry Research Unit and we have been working together since then. As we developed novel tools for the problems from quantum chemistry, we realized these same tools could be applied to study the spectra of large T?plitz matrices, which are of considerable interest in several areas of pure and applied mathematics. This is a satisfying illustration of the advantages of interdisciplinary research. The Mathematical Chemistry Research Unit was founded by myself and Prof. Paul Mezey after I became involved in some chemistry related problems.

Selected Recent Publications:
1. D. Larson, E. Schulz, D. Speegle and K. Taylor: Explicit Cross sections of Singly Generated Group Actions. Harmonic Analysis and Applications, A volume in honor of John J. Benedetto, C. Heil, ed., Birkhauer, Boston (2006).

2. S. Arimoto, M. Spivakovsky, K.F. Taylor and P.G. Mezey: Proof of the Fukui Conjecture via Resolution of Singularities and Related Methods. II. J. Math. Chem. 37 171-189 (2005).

3. E. Schulz and K. Taylor: Projections in L¹-algebras and Tight Frames. Contemporary Mathematics 363 313-319 (2004).

4. Shigeru Arimoto, Mark Spivakovsky, Hiromu Ohno, Peter Zizler, Rob A. Zuidwijk, Keith F. Taylor, Tokio Yamabe, and Paul G. Mezey: Structural Analysis of Certain Linear Operators Representing Chemical Network Systems via the Existence and Uniqueness Theorems of Spectral Resolution. VII. International J. of Quantum Chemistry 97 765-775 (2004).

5. L.-H. Lim, J. Packer, and K. Taylor: A Direct Integral Decomposition of the Wavelet Representation. Proc. Amer. Math. Soc. 129 3057-3067(2001).