Abstract harmonic analysis of continuous wavelet transforms
Author(s)
Bibliographic Information
Abstract harmonic analysis of continuous wavelet transforms
（Lecture notes in mathematics, 1863）
Springer, c2005
Available at 65 libraries
Note
Includes bibliographical references (p. [185]-190) and index
Description and Table of Contents
Description
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 volume can also be read as a problem-driven introduction to the Plancherel formula.
Table of Contents
Introduction.- Wavelet Transforms and Group Representations.- The Plancherel Transform for Locally Compact Groups.- Plancherel Inversion and Wavelet Transforms.- Admissible Vectors for Group Extension.- Sampling Theorems for the Heisenberg Group.- References.- Index.
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