Nonstandard Methods in Commutative Harmonic Analysis
Book Details
Format
Hardback or Cased Book
Book Series
Translations of Mathematical Monographs
ISBN-10
0821804197
ISBN-13
9780821804193
Publisher
American Mathematical Society
Imprint
American Mathematical Society
Country of Manufacture
US
Country of Publication
GB
Publication Date
Apr 30th, 1997
Print length
166 Pages
Weight
539 grams
Product Classification:
Calculus & mathematical analysisCalculus and mathematical analysis
Ksh 25,400.00
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Discusses nonstandard analysis (NSA) and its applications to harmonic analysis on locally compact Abelian (LCA) groups. This monograph introduces a notion of approximation of topological groups by finite groups. It also includes basic concepts of NSA.
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.
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