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Wavelet Analysis and Applications
Edited by: Donggao Deng, Zhongshan University, Guangzhou, People's Republic of China, Daren Huang, Zhejiang University, Hangzhou, People's Republic of China, Rong-Qing Jia, University of Alberta, Edmonton, AB, Canada, Wei Lin, Zhongshan University, Guangzhou, People's Republic of China, and Jianzhong Wang, Sam Houston State University, Huntsville, TX
A co-publication of the AMS and International Press.

AMS/IP Studies in Advanced Mathematics
2002; 326 pp; softcover
Volume: 25
ISBN-10: 0-8218-2991-2
ISBN-13: 978-0-8218-2991-2
List Price: US$64
Member Price: US$51.20
Order Code: AMSIP/25
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Wavelet analysis has been one of the major research directions in science in the last decade. More and more mathematicians and scientists join this exciting research area. Certainly, wavelet analysis has had a great impact in areas such as approximation theory, harmonic analysis, and scientific computation. More importantly, wavelet analysis has shown great potential in applications to information technology such as signal processing, image processing, and computer graphics.

China has played a significant role in this development of wavelet analysis as evidenced by many fruitful theoretical results and practical applications. A conference on wavelet analysis and its applications was organized to exchange ideas and results with international research groups at Zhongshan University (Guangzhou, China). This volume contains the proceedings from that conference.

Comprised here are selected papers from the conference, covering a wide range of research topics of current interest. Many significant results are included in the study of refinement equations and refinable functions, properties and construction of wavelets, spline wavelets, multi-wavelets, wavelet packets, shift-invariant spaces, approximation schemes and subdivision algorithms, and tilings. Several papers also focus on applications of wavelets to numerical solutions of partial differential equations and integral equations, image processing and facial recognition, computer vision, and feature extraction from data.

Titles in this series are co-published with International Press, Cambridge, MA.


Graduate students and research mathematicians interested in wavelets and applications.

Table of Contents

  • A. Aldroubi, Q. Sun, and W.-S. Tang -- Non-uniform sampling in multiply generated shift-invariant subspaces of \(L^p(\mathbb{R}^d)\)
  • R. Ashino, C. Heil, M. Nagase, and R. Vaillancourt -- Multiwavelets, pseudodifferential operators and microlocal analysis
  • S. Basu, C. A. Micchelli, and P. Olsen -- A maximum entropy criterion for feature extraction
  • O. Bratteli and P. E. T. Jorgensen -- Wavelet filters and infinite-dimensional unitary groups
  • G. J. Chae, H. O. Kim, and R. Y. Kim -- On the Cohen-type conditions for the stabiltiy of shifts of a refinable function
  • W. Chen and W. Lin -- Trigonometric Hermite wavelet and natural integral equations for Stokes problem
  • D.-Q. Dai -- Vision, harmonic oscillator and wavelets
  • T. N. T. Goodman and S. L. Lee -- Some properties of refinable splines
  • L. Gori and F. Pitolli -- On some applications of a class of totally positive bases
  • B. Han and S. D. Riemenschneider -- Interpolatory biorthogonal wavelets and CBC algorithm
  • D. P. Hardin and T. A. Hogan -- Constructing orthogonal refinable function vectors with prescribed approximation order and smoothness
  • D. Huang, Z. Wang, and Z. Zhang -- On M-band wavelets having three vanishing moments
  • R.-Q. Jia and Q.-T. Jiang -- Approximation power of refinable vectors of functions
  • J. Ning -- Wavelet decomposition under translate
  • H. O. Kim and J. K. Lim -- Applications of shift-invariant space theory to some problems of multi-resolution analysis of \(L^2({\mathbb R}^d)\)
  • I. Kirat and K.-S. Lau -- On the connectedness and classification of self-affine tiles
  • X.-z. Liang and M.-c. Liu -- Wavelet-Galerkin methods for second kind integral equations
  • S. Li -- Convergence of cascade algorithms in \(L_p (0\leq p \leq 1)\)
  • I. Ya. Novikov -- Asymptotics of zeros of Bernstein polynomials that are related to modified Daubechies wavelets
  • Q. Sun -- Homogeneous and nonhomogeneous refinable distributions in \(F^{q,\gamma}\)
  • J. Tang, S. Kawato, and J. Ohya -- A wavelet transform based face recognition system and its applications
  • J. Wang -- Spline wavelets in numerical resolution of partial differential equations
  • M. V. Wickerhauser -- Basis and convergence properties of wavelet packets
  • L. Yang and Y. Y. Tang -- A wavelet-based characterization of curves
  • P. C. Yuen, G. C. Feng, J. H. Lai, and D. Q. Dai -- Face processing and recognition technology
  • D.-X. Zhou -- The \(p\)-norm joint spectral radius and its applications in wavelet analysis
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