Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 / / Gilles Pisier, Michael B. Marcus
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| Autore: |
Marcus Michael B.
|
| Titolo: |
Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 / / Gilles Pisier, Michael B. Marcus
|
| Pubblicazione: | Princeton, NJ : , : Princeton University Press, , [2016] |
| ©1982 | |
| Descrizione fisica: | 1 online resource (161 pages) |
| Disciplina: | 515/.2433 |
| Soggetto topico: | Fourier series |
| Harmonic analysis | |
| Soggetto non controllato: | Abelian group |
| Almost periodic function | |
| Almost surely | |
| Banach space | |
| Big O notation | |
| Cardinality | |
| Central limit theorem | |
| Circle group | |
| Coefficient | |
| Commutative property | |
| Compact group | |
| Compact space | |
| Complex number | |
| Continuous function | |
| Corollary | |
| Discrete group | |
| Equivalence class | |
| Existential quantification | |
| Finite group | |
| Fourier series | |
| Gaussian process | |
| Haar measure | |
| Harmonic analysis | |
| Independence (probability theory) | |
| Inequality (mathematics) | |
| Integer | |
| Irreducible representation | |
| Non-abelian group | |
| Non-abelian | |
| Normal distribution | |
| Orthogonal group | |
| Orthogonal matrix | |
| Probability distribution | |
| Probability measure | |
| Probability space | |
| Probability | |
| Random function | |
| Random matrix | |
| Random variable | |
| Rate of convergence | |
| Real number | |
| Ring (mathematics) | |
| Scientific notation | |
| Set (mathematics) | |
| Slepian's lemma | |
| Small number | |
| Smoothness | |
| Stationary process | |
| Subgroup | |
| Subset | |
| Summation | |
| Theorem | |
| Uniform convergence | |
| Unitary matrix | |
| Variance | |
| Persona (resp. second.): | PisierGilles |
| Note generali: | Bibliographic Level Mode of Issuance: Monograph |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 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 |
| Sommario/riassunto: | 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 of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research. |
| Titolo autorizzato: | Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 |
| ISBN: | 1-4008-8153-6 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910154747303321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Annals of mathematics studies ; ; Number 101.