Convolution Operators on Groups

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This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on Lp spaces, arriving at a description of these operators and Lp versions of the theorems of Wiener and Kaplansky-Helson.

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Title Statements

Full title :Convolution Operators on Groups.

Summary

Edition Statements

Publication Date:2011.

Publication Statements

Publisher(s):Springer Berlin Heidelberg
Place of Publication:Berlin, Heidelberg
Language:eng
Publication Date:2011.

The Physical Object

Description:1 online resource (181 pages).

Edition Identifiers

ISBN:3642206557, 9783642206559
DOI:10.1007/978-3-642-20656-6
oclc:ocn990648409
LC Classification:QA3
Dewey Decimal:512.46

2.2 A Commutation Property of CV2(G)2.3 An Approximation Theorem for CV2(G); Chapter 3 : The Figa-Talamanca Herz Algebra; 3.1 Definition of Ap(G); 3.2 A2(G) for G Abelian; 3.3 Ap(G) is a Banach Algebra; Chapter 4 : The Dual of Ap(G); 4.1 The Dual of Ap(G): The Notion of Pseudomeasure; 4.2 Applications to Abelian Groups; 4.3 Holomorphic Functions Operating on Ap(G); Chapter 5 : CVp(G) as a Module on Ap(G); 5.1 The Convolution Operator (k*Ĭ)T; 5.2 The Convolution Operator uT; 5.3 CVp(G) as a Module on Ap(G); 5.4 Approximation of T by (k*Ĭ)T for an Amenable G.

Chapter 6 : The Support of a Convolution Operator6.1 Definition of the Support of a Convolution Operator; 6.2 Characterization of the Support of a Pseudomeasure; 6.3 A Generalization of Wiener's Theorem; 6.4 An Approximation Theorem; 6.5 Application to Amenable Groups; Chapter 7 : Convolution Operators Supportedby Subgroups; 7.1 The Image of a Convolution Operator; 7.2 On the Operator i(T); 7.3 A Canonical Isometry of CVp(H) into CVp(G); 7.4 The Support of i(T); 7.5 Theorems of de Leeuw and Saeki; 7.6 The Image of the Map i; 7.7 First Applications: The Theorem of Kaplansky-Helson.