**Translations of Mathematical Monographs**

1997;
166 pp;
Hardcover

MSC: Primary 43; 03; 26;
Secondary 28; 47; 42; 22; 54; 46

**Print ISBN: 978-0-8218-0419-3
Product Code: MMONO/164**

List Price: $95.00

Individual Member Price: $76.00

# Nonstandard Methods in Commutative Harmonic Analysis

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*E. I. Gordon*

This monograph discusses nonstandard analysis (NSA) and its applications to harmonic analysis on locally compact Abelian (LCA) groups. A new notion of approximation of topological groups by finite groups is introduced and investigated. Based on this notion, new results are obtained on convergence of finite Fourier transformations (FT) to the FT on an LCA group. These results, formulated in standard terms in the Introduction, are proved by means of NSA. The book also includes new results on the theory of relatively standard elements and extensions of results of \(S\)-integrable liftings in Loeb measure spaces to the case of \(\sigma\)-finite Loeb measures. Basic concepts of NSA are included.

#### Table of Contents

# Table of Contents

## Nonstandard Methods in Commutative Harmonic Analysis

#### Readership

Graduate students and research mathematicians interested in mathematical analysis and mathematical and functional analysis, theoretical physicists and computer scientists.

#### Reviews

Perfectly suited for running a study group among a number of professional mathematicians and senior students willing to start from scratch and to develop a working knowledge of nonstandard analysis taking them right to the cutting edge of current research.

-- Mathematical Reviews