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  • Book
  • © 2008

Representations, Wavelets, and Frames

A Celebration of the Mathematical Work of Lawrence W. Baggett

Birkhäuser
  • Contributed volume comprised of the work of prominent researchers

  • Discusses both theoretical and applied harmonic analysis including, wavelets and frames

  • Includes recent applications to problems in sampling theory and image compression

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

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eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-0-8176-4683-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 149.00
Price excludes VAT (USA)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xl
  2. Classical and Abstract Harmonic Analysis

    1. Some Riemann Sums Are Better Than Others

      • Victor W. Guillemin, Daniel W. Stroock
      Pages 3-12
    2. Gelfand Pairs Associated with Finite Heisenberg Groups

      • Chal Benson, Gail Ratcliff
      Pages 13-31
    3. Groups with Atomic Regular Representation

      • Keith F. Taylor
      Pages 33-45
  3. Wavelet Sets

    1. Simple Wavelet Sets for Scalar Dilations in ℝ2

      • Kathy D. Merrill
      Pages 177-192
    2. Interpolation Maps and Congruence Domains for Wavelet Sets

      • Xiaofei Zhang, David R. Larson
      Pages 193-214
  4. Applications to Dynamical Systems and C*-Algebras

    1. Orthogonal Exponentials for Bernoulli Iterated Function Systems

      • Palle E. T. Jorgensen, Keri Kornelson, Karen Shuman
      Pages 217-237
  5. Signal and Image Processing

    1. Entropy Encoding in Wavelet Image Compression

      • Myung-Sin Song
      Pages 293-311
  6. Back Matter

    Pages 313-322

About this book

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

  • Department of Mathematics, The University of Iowa, Iowa City, USA

    Palle E. T. Jorgensen

  • Department of Mathematics, Colorado College, Colorado Springs, USA

    Kathy D. Merrill

  • Department of Mathematics, University of Colorado at Boulder, Boulder, USA

    Judith A. Packer

Bibliographic Information

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-0-8176-4683-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 149.00
Price excludes VAT (USA)