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Nonstandard Methods in Commutative Harmonic Analysis (Translations of Mathematical Monographs) 🔍
Evgenij I Gordon Providence, R.I.: American Mathematical Society, American Mathematical Society, [N.p.], 2018
English [en] · PDF · 12.5MB · 2018 · 📗 Book (unknown) · 🚀/ia · Save
description
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.
Alternative author
Gordon, E. I. (evgenii Izrailevich) , 1949-
Alternative author
Eugenii I Gordon
Alternative edition
Translations of mathematical monographs,, v. 164, Providence, R.I, Rhode Island, 1997
Alternative edition
United States, United States of America
Alternative edition
Volume 164, 1997
metadata comments
Includes bibliographical references (p. 163-166).
Translated from the original Russian manuscript.
Alternative description
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.
Alternative description
xiv, 166 p. ; 26 cm
Translated from the original Russian manuscript
Includes bibliographical references (p. 163-166)
Alternative description
E.i. Gordon. Translated From The Original Russian Manuscript. Includes Bibliographical References (p.163-166).
date open sourced
2023-06-28
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