Fourier and Fourier-Stieltjes algebras on locally compact groups / Eberhard Kaniuth, Anthony To-Ming Lau.

Format:

Book

Author/Creator:

Kaniuth, Eberhard, author.

Lau, Anthony To-Ming, author.

Series:

Mathematical surveys and monographs ; no. 231.

Mathematical surveys and monographs ; volume 231

Language:

English

Subjects (All):

Topological groups.

Group algebras.

Banach algebras.

Fourier analysis.

Stieltjes transform.

Locally compact groups.

Physical Description:

xi, 306 pages ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists.

Contents:

Preliminaries

Basic theory of Fourier and Fourier-Stieltjes algebras

Miscellaneous further topics

Amenability properties of A(G) and B(G)

Multiplier algebras of Fourier algebras

Spectral synthesis and ideal theory

Extension and separation properties of positive definite functions.

Notes:

Includes bibliographical references (pages 291-302) and index.

ISBN:

9780821853658

0821853651

OCLC:

1019834450