陶伯理论:百年进展:A century of developments 本书特色

陶伯理论对级数和积分的可求和性判定的不同方法加以比较，确定它们何时收敛，给出渐近估计和余项估计。由陶伯理论的*初起源开始，作者介绍该理论的发展历程：他的专业评论再现了早期结果所引来的兴奋；论及困难而令人着迷的哈代一李特尔伍德定理及其出人意料的一个简洁证明；高度赞扬维纳基于傅里叶理论的突破，引人人胜的“高指数”定理以及应用于概率论的Karamata正则变分理论。作者也提及盖尔范德对维纳理论的代数处理以及其本人的分布方法。介绍了博雷尔方法和“圆”方法的一个统一的新理论，《国外数学名著系列（影印版）36：陶伯理论 百年进展》还讨论了研究素定理的各种陶伯方法。书后附有大量参考文献和详尽的索引。

陶伯理论:百年进展:A century of developments 内容简介

陶伯理论对级数和积分的可求和性判定的不同方法加以比较, 确定它们何时收敛, 给出渐近估计和余项估计。

陶伯理论:百年进展:A century of developments 目录

Ⅰ The Hardy-Littlewood Theorems
1 Introduction
2 Examples of Summability Methods AbeliaTheorems and TauberiaQuestion
3 Simple Applications of Cesa(')ro， Abel and Borel Summability
4 Lambert Summability iNumber Theory
5 Tauber's Theorems for Abel Summability
6 TauberiaTheorem for Cesa(')ro Summability
7 Hardy-Littlewood Tauberians for Abel Summability
8 Tauberians Involving Dirichlet Series
9 Tauberians for Borel Summability
10 Lambert Tauberiaand Prime Number Theorem
11 Karamata's Method for Power Series
12 Wielandt's Variatioothe Method
13 Transitiofrom Series to Integrals
14 Extensioof Tauber's Theorems to Laplace-Stieltjes Transforms
15 Hardy-Littlewood Type Theorems Involving Laplace Transforms
16 Other TauberiaConditions： Slowly Decreasing Functions
17 Asymptotics for Derivatives
18 Integral Tauberians for Cesa(')ro Summability
19 The Method of the Monotone Minorant
20 Boundedness Theorem Involving a General-Kernel Transform
21 Laplace-Stieltjes and Stieltjes Transform
22 General Dirichlet Series
23 The High-Indices Theorem
24 Optimality of TauberiaConditions
25 TauberiaTheorems of Nonstandard Type
26 Important Properties of the Zeta Function

Ⅱ Wiener's Theory
1 Introduction
2 Wiener Problem： Pitt's Form
3 Testing Equatiofor Wiener Kernels
4 Original Wiener Problem
5 Wiener's Theorem With Additions by Pitt
6 Direct Applications of the Testing Equations
7 Fourier Analysis of Wiener Kernels
8 The Principal Wiener Theorems
9 Proof of the DivisioTheorem
10 Wiener Families of Kernels
11 Distributional Approach to Wiener Theory
12 General Tauberiafor Lambert SummabilitY
13 Wiener's 'Second TauberiaTheorem'
14 A Wiener Theorem for Series
15 Extensions
16 Discussioof the TauberiaConditions
17 Landau-Ingham Asymptotics
18 Ingham Summability
19 Applicatioof Wiener Theory to Harmonic Functions

Ⅲ Complex TauberiaTheorems
1 Introduction
2 A Landau-Type Tauberiafor Dirichlet Series
3 MelliTransforms
4 The Wiener-Ikehara Theorem
5 Newer Approach to Wiener-Ikehara
6 Newman's Way to the PNT． Work of Ingham
7 Laplace Transforms of Bounded Functions
8 Applicatioto Dirichlet Series and the PNT
9 Laplace Transforms of Functions Bounded From Below
10 TauberiaConditions Other ThaBoundedness
11 AOptimal Constant iTheorem 10．1
12 Fatou and Riesz． General Dirichlet Series
13 Newer Extensions of Fatou-Riesz
14 PseudofunctioBoundary Behavior
15 Applications to Operator Theory
16 Complex Remainder Theory
17 The Remainder iFatou's Theorem
18 Remainders iHardy-Littlewood Theorems Involving Power Series
19 A Remainder for the Stieltjes Transform

Ⅳ Karamata's Heritage： Regular Variation
1 Introduction
2 Slow and Regular Variation
3 Proof of the Basic Properties
4 Possible Pathology
5 Karamata's Characterizatioof Regularly． Varying Functions
6 Related Classes of Functions

 1/2    1 2 下一页 尾页

自然科学 数学 数学理论

在线阅读