Almost Periodic Type Functi*** and Ergodicity概周期型函数和遍历性(精) pdf 免费 地址 txt lrf 下载 kindle umd

This book provides a comprehensive theory of almost periodic type functi*** with a large number of the applicati*** to differential equati***，functional equati*** and evolution equati***. In addition，it also presents a basic theory on ergodicity and its applicati*** in the theory of function spectrum，semi group of bounded linear operators and dynamical systems。It reflects new establishment of recent years in the field。This monograph is self-contained，the only prerequisite being a basic knowledge of functional ***ysis and ordinary differential equati***。It is written for the mathematicians who wish to learn about the subject and is of interest to the specialists in the areas of abstract harmonic ***ysis，functional ***ysis，differential (functional) equati***，dynamical system and ergodicity。It is also suitable as a textbook for graduates in Mathematical Analysis。

Preface

Chapter 1 Almost periodic type functi***

　1.1 Almost periodic functi***

　　1.1.1 Numerical almost periodic functi***

　　1.1.2 Uniform almost periodic functi***

　　1.1.3 Vector-valued almost periodic functi***

　1.2 Asymptotically almost periodic functi***

　1.3 Weakly almost periodic functi***

　　1.3.1 Vector-valued weakly almost periodic functi***

　　1.3.2 Ergodic theorem

　　1.3.3 Invariant mean and mean convolution

　　1.3.4 Fourier series of WAP(R,H)

　　1.3.5 Uniformly weakly almost periodic functi***

　1.4 Approximate theorem and applicati***

　　1.4.1 Numerical approximate theorem

　　1.4.2 Vector-valued approximate theorem

　　1.4.3 Unique decomposition theorem

　1.5 Pseudo almost periodic functi***

　　1.5.1 Pseudo almost periodic functi***

　　1.5.2 Generalized pseudo almost periodic functi***

　1.6 Converse problems of Fourier expansi***

　1.7 Almost periodic type sequences

　　1.7.1 Almost periodic sequences

　　1.7.2 Other almost periodic type sequences

Chapter 2 Almost periodic type differential equati***

　2.1 Linear differential equati***

　　2.1.1 Ordinary differential equati***

　　2.1.2 Abstract differential equati***

　　2.1.3 Integration of almost periodic type functi***

　2.2 Partial differential equati***

　　2.2.1 Dirichlet Problems

　　2.2.2 Parabolic equati***

　　2.2.3 Second-order equati*** with gradient operators

　2.3 Means，introversion and nonlinear equati***

　　2.3.1 General theory of means and introversi***

　　2.3.2 Applicati*** to (weakly) almost periodic functi***

　　2.3.3 Nonlinear differential equati***

　　2.3.4 Implicati*** of almost periodic type soluti***

　2.4 Regularity and exponential dic***omy

　　2.4.1 General theory of regularity

　　2.4.2 Stability of regularity

　　2.4.3 Almost periodic

　2.5 Equati*** with piecewise c***tant argument

　　2.5.1 Exponential dic***omy for difference equati***

　　5.2.2 Equati*** with piecewise c***tant argument

　　5.2.3 Almost periodic difference equati***

　2.6 Equati*** with unbounded forcing term

　2.7 Almost periodic structural stability

　　2.7.1 Topological equivalence and structural stability

　　2.7.2 Exponential dic***omy and structural stability

Chapter 3 Ergodicity and abstract difference equati***

　3.1 Ergodicity and regularity

　　3.1.1 Ergodicity and regularity

　　3.1.2 Soluti*** of almost periodic type equati***

　3.2 Ergodicity and nonlinear equati***

　3.3 Semigroup of operators and applicati***

　　3.3.1 Semigroup of operators

　　3.3.2 Almost periodic type soluti***

　3.4 Delay difference equati***

　　3.4.1 Introduction of delay difference equati***

　　3.4.2 Linear autonomous equati***

　　3.4.3 Linear nonautonomous equati***

　3.5 Spectrum of functi***

　3.6 Abstract Cauchy Problems

　　3.6.1 Harmonic ***ysis of soluti***

　　3.6.2 Asymptotic behavior of soluti***

　　3.6.3 Mild soluti***

　　3.*** Weakly almost periodic soluti***

Chapter 4 Ergodicity and averaging methods

　4.1 Ergodicity and its properties

　4.2 Quantitative theory

　　4.2.1 Introduction

　　4.2.2 Quantitative theory of averaging methods

　　4.2.3 Example and comments

　4.3 Perturbati*** of noncritical linear systems

　　4.4.1 Almost periodic type soluti*** of nonlinear equati***

　　4.4.2 Some examples

　4.5 Averaging methods for functional equati***

　　4.5.1 Averaging methods for functional differential equati***

　　4.5.2 Averaging methods for delay difference equati***

Bibliography

Notati***

Index

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书籍介绍

《Almost Periodic Type Functi*** and Ergodicity》为我们提供了大量的应用微分方程，泛函方程和演化方程的概周期型功能全面的理论。此外，它也提出了关于遍历性和功能谱，界线性算子半群和动力系统理论及其应用的基本理论。它反映了近年来在该领域建立新的。这本专着是自包含的，在唯一的先决条件是一个功能分析和常微分方程的基本知识。这是写的数学家谁想要了解的主题和兴趣，抽象调和分析，功能分析，微分（功能）方程等领域的专家是，动力系统和遍历性。