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Representations, Wavelets, and Frames

A Celebration of the Mathematical Work of Lawrence W. Baggett

  • Palle E. T. Jorgensen
  • Kathy D. Merrill
  • Judith A. Packer

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xl
  2. Classical and Abstract Harmonic Analysis

    1. Victor W. Guillemin, Daniel W. Stroock
      Pages 3-12
    2. Chal Benson, Gail Ratcliff
      Pages 13-31
    3. Keith F. Taylor
      Pages 33-45
  3. Frames and Multiresolution Structures

  4. Wavelet Sets

    1. Kathy D. Merrill
      Pages 177-192
    2. Xiaofei Zhang, David R. Larson
      Pages 193-214
  5. Applications to Dynamical Systems and C*-Algebras

  6. Signal and Image Processing

  7. Back Matter
    Pages 313-322

About this book

Introduction

Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis).

Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers.

The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions.

Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang.

Keywords

Gelfand pair Interpolation Symbol communication harmonic analysis image processing signal analysis

Editors and affiliations

  • Palle E. T. Jorgensen
    • 1
  • Kathy D. Merrill
    • 2
  • Judith A. Packer
    • 3
  1. 1.Department of MathematicsThe University of IowaIowa CityUSA
  2. 2.Department of MathematicsColorado CollegeColorado SpringsUSA
  3. 3.Department of MathematicsUniversity of Colorado at BoulderBoulderUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4683-7
  • Copyright Information Birkhäuser Boston 2008
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4682-0
  • Online ISBN 978-0-8176-4683-7
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site
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