Abstract Harmonic Analysis of Continuous Wavelet Transforms

Hartmut Führ (auth.)3540242597, 9783540242598

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.

Table of contents :
1. Introduction….Pages 1-13
2. Wavelet Transforms and Group Representations….Pages 15-58
3. The Plancherel Transform for Locally Compact Groups….Pages 59-103
4. Plancherel Inversion and Wavelet Transforms….Pages 105-138
5. Admissible Vectors for Group Extensions….Pages 139-168
6. Sampling Theorems for the Heisenberg Group….Pages 169-184
References and Index….Pages 185-193