Nonstandard methods in commutative harmonic analysis
著者
書誌事項
Nonstandard methods in commutative harmonic analysis
（Translations of mathematical monographs, v. 164）
American Mathematical Society, c1997
- タイトル別名
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Нестандартные методы в некоммутативном гармоническом анализе / Е.И. Гордон
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注記
Translated from the original Russian manuscript by H.H. McFaden
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
Introduction Basic concepts of nonstandard analysis Nonstandard analysis of operators acting in spaces of measurable functions Nonstandard analysis of locally compact Abelian groups Bibliography.
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