Abstract Harmonic Analysis of Continuous Wavelet Transforms

  • Authors
  • Hartmut Führ
Part of the Lecture Notes in Mathematics book series (LNM, volume 1863)

Table of contents

  1. Front Matter
    Pages N2-X
  2. Hartmut Führ
    Pages 1-13
  3. Hartmut Führ
    Pages 139-168
  4. Hartmut Führ
    Pages 169-184
  5. Hartmut Führ
    Pages 185-190
  6. Back Matter
    Pages 191-199

About this book

Introduction

This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the book can also be read as a problem-driven introduction to the Plancherel formula.

Keywords

Heisenberg group Plancherel theory continuous wavelet transforms harmonic analysis sampling theory

Bibliographic information

  • DOI https://doi.org/10.1007/b104912
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-24259-8
  • Online ISBN 978-3-540-31552-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book