《Tauberian Theorems》

作者	H.R.Pitt 编者
出版	Oxford University press
参考页数	174
出版时间	1958（求助前请核对）目录预览
ISBN号	无 — 求助条款
PDF编号	818144768（仅供预览，未存储实际文件）
求助格式	扫描PDF（若分多册发行，每次仅能受理1册）

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Ⅰ．INTRODUCTION1

1．1Abelian transformations1

1．2 Tauberian theorems2

1．3 Mercerian theorems4

1．4 miscellaneous tauberian theorems and the prime number theorem4

Ⅱ．ELEMENTARY TAUBERIAN THEOREMS6

2．1Tauberian conditions6

2．2 Elementary general tauberian theorems17

Ⅲ．CLASSICAL TAUBERIAN THEOREMS29

3．1Transformation of the kernel29

3．2 Cesaro and Riesz summation30

3．3 Abel summation34

3．4 Borel summation37

Ⅳ．WIENER＇S THEORY43

4．1Fourier integrals43

4．2 Wiener＇s tauberian theorems50

4．3 Some extensions of Wiener＇s theorems57

4．4 Application to special tauberian theorems78

Ⅴ．MERCERIAN THEOREMS93

5．1Fourier-Stieltjes transforms93

5．2 General mercerian theorems114

5．3 Some special mercerian theorems121

5．4 Further extensions and applications to integrodifferential equations126

Ⅵ．TAUBERIAN THEOREMS AND THE PRIME NUMBER THEOREM130

6．1The Landau-Ikehara theorem130

6．2 Classical proofs of the prime number theorem138

6．3 The elementary proof of the prime number theorem and related tauberian theorems152

BIBLIOGRAPHY167

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高度相关资料

: Strong limit theorems; 1992 Science Press

: APPROXIMATION THEOREMS OF MATHEMATICAL STATISTICS

: Tauberian Theorems for Generalized Functions

: fourier theorems 1987

: Closed graph theorems and webbed spaces; 1978 Pitman

: Minimax Theorems; 1996 Birkhauser

: LIMIT THEOREMS FOR STOCHASTIC PROCESSES; 1987 SPRINGER-VERLAG

: RANDOM NUMBER GENERATION AND QUASI-MONTE CARLO METHODS; 1992 SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS

: Stochastic space-time models and limit theorems; 1985 D. Reidel Pub. Co. : Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers