泛函不等式,马尔可夫半群与谱理论

基本信息

丛书名：当代杰出青年科学文库

作者：王凤雨

出版社：科学出版社

出版日期：2006-12

ISBN：7030144155

版次：1

页数：379页

字数：390

开本：小16开

包装：精装

内容简介

In this book, we introduce functional inequalities to describe:

(i) the spectrum of the generator: the essential and discrete spectrums,high order eigenvalues, the principal eigenvalue, and the spectral gap;

(ii) the semigroup properties: the uniform integrability, the compactness,the convergence rate, and the existence of density;

(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetric inequality, and the transportation cost inequality.

作者简介

姓名：王凤雨

作品：《泛函不等式,马尔可夫半群与谱理论》

目录

Contents

Chapter 0 Preliminaries

0.1 Dirichlet forms, sub-Markov semigroups and generators

0.2 Dirichlet forms and Markov processes

0.3 Spectral theory

0.4 Riemannian geometry

Chapter 1 Poincaré Inequality and Spectral Gap

1.1 A general result and examples

1.2 Concentration of measures

1.3 Poincaré inequalities for jump processes

1.3.1 The bounded jump case

1.3.2 The unbounded jump case

1.3.3 A criterion for birth-death processes

1.4 Poincaré inequality for diffusion processes

1.4.1 The one-dimensional case

1.4.2 Spectral gap for diffusion processes on R上标d

1.4.3 Existence of the spectral gap on manifolds and application to nonsymmetric elliptic operators

1.5 Notes

Chapter 2 Diffusion Processes on Manifolds and Applications

2.1 Kendall-Cranston''s coupling

2.2 Estimates of the first (closed and Neumann) eigenvalue

2.3 Estimates of the first two Dirichlet eigenvalues

2.3.1 Estimates of the first Dirichlet eigenvalue

2.3.2 Estimates of the se