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Nonstandard Methods in Commutative Harmonic Analysis

E. I. Gordon Nizhny Novgorod State University, Russia
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Hardcover ISBN: 978-0-8218-0419-3
Product Code: MMONO/164
List Price: $101.00 MAA Member Price:$90.90
AMS Member Price: $80.80 Electronic ISBN: 978-1-4704-4579-9 Product Code: MMONO/164.E List Price:$95.00
MAA Member Price: $85.50 AMS Member Price:$76.00
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List Price: $151.50 MAA Member Price:$136.35
AMS Member Price: $121.20 Click above image for expanded view Nonstandard Methods in Commutative Harmonic Analysis E. I. Gordon Nizhny Novgorod State University, Russia Available Formats:  Hardcover ISBN: 978-0-8218-0419-3 Product Code: MMONO/164  List Price:$101.00 MAA Member Price: $90.90 AMS Member Price:$80.80
 Electronic ISBN: 978-1-4704-4579-9 Product Code: MMONO/164.E
 List Price: $95.00 MAA Member Price:$85.50 AMS Member Price: $76.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$151.50 MAA Member Price: $136.35 AMS Member Price:$121.20
• Book Details

Translations of Mathematical Monographs
Volume: 1641997; 166 pp
MSC: Primary 43; 03; 26; Secondary 28; 47; 42; 22; 54;

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.

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

• Chapters
• Introduction
• Chapter 0. basic concepts of nonstandard analysis
• Chapter 1. Nonstandard analysis of operators acting in spaces of measurable functions
• Chapter 2. Nonstandard analysis on locally compact Abelian groups
• 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.

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Volume: 1641997; 166 pp
MSC: Primary 43; 03; 26; Secondary 28; 47; 42; 22; 54;

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.