《泛函不等式，馬爾可夫半群與譜理論》是2006年科學出版社出版的圖書，由王鳳雨編寫。本書的主要內容涉及機率論、泛函分析、微分幾何和統計物理等多個學科，較系統的介紹了近十年有關泛函不等式及其近十年來的有關泛函不等式及其套用的主要研究成果和研究方法。
基本介紹
- 書名：泛函不等式,馬爾可夫半群與譜理論
- 作者：王鳳雨
- 出版社：科學出版社
- 出版時間：2006-12
基本信息,內容簡介,作者簡介,目錄,
基本信息
ISBN：7030144155
版次：1
頁數：379頁
字數：390
開本：小16開
包裝：精裝
內容簡介
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.
作者簡介
姓名：王鳳雨
作品：《泛函不等式,馬爾可夫半群與譜理論》
目錄
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上標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
