Random fourier series with applications to harmonic analysis:
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 un...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
[1981]
|
| Series: | Annals of Mathematics Studies
number 101 |
| Subjects: | |
| Online Access: | Volltext |
| Summary: | 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 |
| Item Description: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Physical Description: | 1 online resource |
| ISBN: | 9781400881536 |
| DOI: | 10.1515/9781400881536 |
Staff View
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| 245 | 1 | 0 | |a Random fourier series with applications to harmonic analysis |c Gilles Pisier, Michael B. Marcus |
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| 264 | 4 | |c © 1981 | |
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| 490 | 1 | |a Annals of Mathematics Studies |v number 101 | |
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a 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 | ||
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| 650 | 4 | |a Fourier series | |
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Record in the Search Index
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| bvnumber | BV043712413 |
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV043712413 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400881536 |
| language | English |
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| publishDate | 1981 |
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| publisher | Princeton University Press |
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| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Marcus, Michael B. (DE-588)1132226228 aut Random fourier series with applications to harmonic analysis Gilles Pisier, Michael B. Marcus Princeton, NJ Princeton University Press [1981] © 1981 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 101 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) 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 In English Fourier series Harmonic analysis Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 s Stochastischer Prozess (DE-588)4057630-9 s Harmonische Analyse (DE-588)4023453-8 s 1\p DE-604 Pisier, Gilles 1950- (DE-588)113782268 aut Erscheint auch als Druck-Ausgabe 0-691-08289-8 Annals of Mathematics Studies number 101 (DE-604)BV040389493 101 https://doi.org/10.1515/9781400881536?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Marcus, Michael B. Pisier, Gilles 1950- Random fourier series with applications to harmonic analysis Annals of Mathematics Studies Fourier series Harmonic analysis Fourier-Reihe (DE-588)4155109-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4155109-6 (DE-588)4057630-9 (DE-588)4023453-8 |
| title | Random fourier series with applications to harmonic analysis |
| title_auth | Random fourier series with applications to harmonic analysis |
| title_exact_search | Random fourier series with applications to harmonic analysis |
| title_full | Random fourier series with applications to harmonic analysis Gilles Pisier, Michael B. Marcus |
| title_fullStr | Random fourier series with applications to harmonic analysis Gilles Pisier, Michael B. Marcus |
| title_full_unstemmed | Random fourier series with applications to harmonic analysis Gilles Pisier, Michael B. Marcus |
| title_short | Random fourier series with applications to harmonic analysis |
| title_sort | random fourier series with applications to harmonic analysis |
| topic | Fourier series Harmonic analysis Fourier-Reihe (DE-588)4155109-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Fourier series Harmonic analysis Fourier-Reihe Stochastischer Prozess Harmonische Analyse |
| url | https://doi.org/10.1515/9781400881536?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT marcusmichaelb randomfourierserieswithapplicationstoharmonicanalysis AT pisiergilles randomfourierserieswithapplicationstoharmonicanalysis |