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Record Nr. |
UNINA9910154747303321 |
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Autore |
Marcus Michael B. |
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Titolo |
Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 / / Gilles Pisier, Michael B. Marcus |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1982 |
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ISBN |
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Descrizione fisica |
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1 online resource (161 pages) |
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Collana |
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Annals of Mathematics Studies ; ; 241 |
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Disciplina |
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Soggetti |
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Fourier series |
Harmonic analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- CONTENTS -- CHAPTER I: INTRODUCTION -- CHAPTER II: PRELIMINARIES -- CHAPTER III: RANDOM FOURIER SERIES ON LOCALLY COMPACT ABELIAN GROUPS -- CHAPTER IV: THE CENTRAL LIMIT THEOREM AND RELATED QUESTIONS -- CHAPTER V: RANDOM FOURIER SERIES ON COMPACT NON-ABELIAN GROUPS -- CHAPTER VI: APPLICATIONS TO HARMONIC ANALYSIS -- CHAPTER VII: ADDITIONAL RESULTS AND COMMENTS -- REFERENCES -- INDEX OF TERMINOLOGY -- INDEX OF NOTATIONS -- Backmatter |
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Sommario/riassunto |
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In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact non-Abelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived.The major results depend heavily on the Dudley-Fernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the non-Abelian case once the proper definition |
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