Random Fourier series with applications to harmonic analysis
著者
書誌事項
Random Fourier series with applications to harmonic analysis
(Annals of mathematics studies, no. 101)
Princeton University Press , University of Tokyo Press, 1981
- : pbk
大学図書館所蔵 全58件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Bibliography: p. 144-147
Includes indexes
内容説明・目次
- 巻冊次
-
ISBN 9780691082899
内容説明
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.
- 巻冊次
-
: pbk ISBN 9780691082929
内容説明
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.
目次
*Frontmatter, pg. i*CONTENTS, pg. v*CHAPTER I: INTRODUCTION, pg. 1*CHAPTER II: PRELIMINARIES, pg. 16*CHAPTER III: RANDOM FOURIER SERIES ON LOCALLY COMPACT ABELIAN GROUPS, pg. 51*CHAPTER IV: THE CENTRAL LIMIT THEOREM AND RELATED QUESTIONS, pg. 65*CHAPTER V: RANDOM FOURIER SERIES ON COMPACT NON-ABELIAN GROUPS, pg. 74*CHAPTER VI: APPLICATIONS TO HARMONIC ANALYSIS, pg. 105*CHAPTER VII: ADDITIONAL RESULTS AND COMMENTS, pg. 122*REFERENCES, pg. 144*INDEX OF TERMINOLOGY, pg. 148*INDEX OF NOTATIONS, pg. 149*Backmatter, pg. 151
「Nielsen BookData」 より