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


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.


Heisenberg group Plancherel theory continuous wavelet transforms harmonic analysis sampling theory

Bibliographic information