1.

Record Nr.

UNINA9910483359003321

Autore

Führ Hartmut

Titolo

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

Pubbl/distr/stampa

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

ISBN

3-540-31552-7

Edizione

[1st ed. 2005.]

Descrizione fisica

1 online resource (X, 193 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1863

Disciplina

515.2433

Soggetti

Harmonic analysis

Fourier analysis

Abstract Harmonic Analysis

Fourier Analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references (pages [185]-190) and index.

Nota di contenuto

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.

Sommario/riassunto

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.