Convolution Operators on Groups

✍ Scribed by Antoine Derighetti (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Tongue: English
Leaves: 185
Series: Lecture Notes of the Unione Matematica Italiana 11
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Elementary Results....Pages 1-23
The Commutation’s Theorem....Pages 25-32
The Figa–Talamanca Herz Algebra....Pages 33-44
The Dual of A p (G)....Pages 45-64
CV p (G) as a Module on A p (G)....Pages 65-84
The Support of a Convolution Operator....Pages 85-99
Convolution Operators Supported by Subgroups....Pages 101-144
CV p (G) as a Subspace of CV 2(G)....Pages 145-160
Back Matter....Pages 161-171

✦ Subjects

Abstract Harmonic Analysis

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