Abstract Harmonic Analysis of Continuous Wavelet Transforms / by Hartmut Führ.

Format:

Book

Author/Creator:

Führ, Hartmut, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1863.

Lecture Notes in Mathematics, 0075-8434 ; 1863

Language:

English

Subjects (All):

Harmonic analysis.

Fourier analysis.

Abstract Harmonic Analysis.

Fourier Analysis.

Local Subjects:

Abstract Harmonic Analysis.

Fourier Analysis.

Physical Description:

1 online resource (X, 193 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783540315520

Access Restriction:

Restricted for use by site license.