《Tauberian Theorems》求取 ⇩

作者 H.R.Pitt 编者
出版 Oxford University press
参考页数 174   ✅ 真实服务 非骗流量  ❤️
出版时间 1958（求助前请核对）  目录预览
ISBN号 无 — 违规投诉 / 求助条款
PDF编号 818144768（学习资料 勿作它用）
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Tauberian Theorems 1958 PDF电子版封面 H.R.Pitt

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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