Nonstandard methods in commutative harmonic analysis

Nonstandard methods in commutative harmonic analysis

by Gordon, E. I., (Evgenii Izrailevich)

Type Book
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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 …

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Title Statements

  • Full title :Nonstandard methods in commutative harmonic analysis / E.I. Gordon.

Summary

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 mea.

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Edition Statements

  • Publication Date:©1997.

Publication Statements

The Physical Object

  • Description:1 online resource

Edition Identifiers

  • ISBN:9781470445799, 1470445794
  • oclc:on1031917997
  • LC Classification:QA403.G67 1997
  • Dewey Decimal:515/.785

Subjects

Analyse harmonique Analyse mathématique non standard Harmonic analysis Nonstandard mathematical analysis

Writers

Gordon, E. I., (Evgenii Izrailevich)

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