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This volume is the first in the series devoted to the commutative harmonic analysis, a fundamental part of the contemporary mathematics. The fundamental nature of this subject, however, has been determined so long ago, that unlike in other volumes of this publication, we have to start with simple notions which have been in constant use in mathematics and physics. Planning the series as a whole, we have assumed that harmonic analysis is based on a small number of axioms, simply and clearly formulated in terms of group theory which illustrate its sources of ideas. However, our subject cannot be completely reduced to those axioms. This part of mathematics is so well developed and has so many different sides to it that no abstract scheme is able to cover its immense concreteness completely. In particular, it relates to an enormous stock of facts accumulated by the classical "trigonometric" harmonic analysis. Moreover, subjected to a general mathematical tendency of integration and diffusion of conventional intersubject borders, harmonic analysis, in its modem form, more and more rests on non-translation invariant constructions. For example, one ofthe most signifi cant achievements of latter decades, which has substantially changed the whole shape of harmonic analysis, is the penetration in this subject of subtle techniques of singular integral operators.
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Contenuti:
I. Methods and Structure of Commutative Harmonic Analysis.- II. Classical Themes of Fourier Analysis.- III. Methods of the Theory of Singular Integrals: Hilbert Transform and Calderón-Zygmund Theory.- Author Index.
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- EditoreSpringer Verlag
- Data di pubblicazione1991
- ISBN 10 3540181806
- ISBN 13 9783540181804
- RilegaturaCopertina rigida
- Numero di pagine284
- RedattoreKhavin V. P., Nikol'Skij N. K.
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Commutative Harmonic Analysis I
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Springer Berlin Heidelberg Aug 1991
(1991)
ISBN 10: 3540181806
ISBN 13: 9783540181804
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Descrizione libro Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numerous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a 'mini-Zygmund' for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail. There is also a thorough introduction to Calderon-Zygmund theory. Dieser Band ist der Anfang der EMS-'Unterreihe' Commutative Harmonic Analysis, in der bisher vier Bände geplant sind. Ein historischer Überblick über Fourieranalysis ist ebenfalls eingeschlossen. Fourieranalysis findet in vielen anderen Fachgebieten der Mathematik Anwendung. 284 pp. Englisch. Codice articolo 9783540181804
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Descrizione libro Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This volume is the first in the series devoted to the commutative harmonic analysis, a fundamental part of the contemporary mathematics. The fundamental nature of this subject, however, has been determined so long ago, that unlike in other volumes of this p. Codice articolo 4883686
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Commutative Harmonic Analysis I : General Survey. Classical Aspects
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Springer Berlin Heidelberg
(1991)
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ISBN 13: 9783540181804
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Descrizione libro Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numerous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a 'mini-Zygmund' for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail. There is also a thorough introduction to Calderon-Zygmund theory. Dieser Band ist der Anfang der EMS-'Unterreihe' Commutative Harmonic Analysis, in der bisher vier Bände geplant sind. Ein historischer Überblick über Fourieranalysis ist ebenfalls eingeschlossen. Fourieranalysis findet in vielen anderen Fachgebieten der Mathematik Anwendung. Codice articolo 9783540181804
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