In this book, the functional inequalities are introduced to describe:. (i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;. (ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;. (iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality

zlibzh/no-category/FENG-YU WANG, Feng-Yu Wang/FUNCTIONAL INEQUATITIES，MARKOV SEMIGROUPS AND SPECTRAL THEORY_30298071.pdf

Functional inequalities, Markov semigroups and spectral theory = Fan han bu deng shi, Ma'erkefu ban qun yu pu li lun

Functional Inequalities Markov Semigroups and Spectral Theory (The Science Series of the Contemporary Elite Youth)

Functional inequalities, Markov semigroups and spectral theory = 泛函不等式, 马尔可夫半群与谱理论

Functional inequalities, Markov Semiqroups and Spectral Theory

王凤雨

Elsevier Science & Technology

Woodhead Publishing Ltd

John Murray Press

SCIENCE PRESS

Focal Press

MyiLibrary

Dang dai jie chu qing nian ke xue wen ku, Dang dai jie chu qing nian ke xue wen ku, Beijing, New York, China, 2005

The Science Series of the Contemporary Elite Youth, Beijing, c2005

Dang dai jie chu qing nian ke xue wen ku, Di 1 ban, Beijing, 2005

Science Series of the Contemporary Elite Youth, Burlington, 2006

Mathematics monograph series (Beijing, China), Beijing, ©2005

Science series of the contemporary elite youth, Beijing, 2006

The Science Series of the Contemporary Elite Youth, 2006

United Kingdom and Ireland, United Kingdom

United States, United States of America

China, People's Republic, China

1 edition, February 24, 2006

1, 20060406

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Includes bibliographical references and index.

Includes bibliographical references (p. 366-375) and index.
Description based on print version record.

Type: 当代图书

Bookmarks:
1. (p1) Chapter 0 Preliminaries
1.1. (p1) 0.1 Dirichlet forms, sub-Markov semigroups and generators
1.2. (p6) 0.2 Dirichlet forms and Markov processes
1.3. (p9) 0.3 Spectral theory
1.4. (p16) 0.4 Riemannian geometry
2. (p24) Chapter 1 Poincaré Inequality and Spectral Gap
2.1. (p24) 1.1 A general result and examples
2.2. (p26) 1.2 Concentration of measures
2.3. (p31) 1.3 Poincaré inequalities for jump processes
2.3.1. (p32) 1.3.1 The bounded jump case
2.3.2. (p35) 1.3.2 The unbounded jump case
2.3.3. (p43) 1.3.3 A criterion for birth-death processes
2.4. (p45) 1.4 Poincaré inequality for diffusion processes
2.4.1. (p45) 1.4.1 The one-dimensional case
2.4.2. (p50) 1.4.2 Spectral gap for diffusion processes on Rd
2.4.3. (p56) 1.4.3 Existence of the spectral gap on manifolds and application to nonsymmetric elliptic operators
2.5. (p64) 1.5 Notes
3. (p67) Chapter 2 Diffusion Processes on Manifolds and Applications
3.1. (p67) 2.1 Kendall-Cranston s coupling
3.2. (p78) 2.2 Estimates of the first(closed and Neumann)eigenvalue
3.3. (p86) 2.3 Estimates of the first two Dirichlet eigenvalues
3.3.1. (p86) 2.3.1 Estimates of the first Dirichlet eigenvalue
3.3.2. (p88) 2.3.2 Estimates of the second Dirichlet eigenvalue and the spectral gap
3.4. (p93) 2.4 Gradient estimates of diffusion semigroups
3.4.1. (p93) 2.4.1 Gradient estimates of the closed and Neumann semigroups
3.4.2. (p97) 2.4.2 Gradient estimates of Dirichlet semigroups
3.5. (p108) 2.5 Harnack and isoperimetric inequalities using gradient estimates
3.5.1. (p108) 2.5.1 Gradient estimates and the dimension-free Harnack inequality
3.5.2. (p111) 2.5.2 The first eigenvalue and isoperimetric constants
3.6. (p114) 2.6 Liouville theorems and couplings on manifolds
3.6.1. (p114) 2.6.1 Liouville theorem using the Brownian radial process
3.6.2. (p116) 2.6.2 Liouville theorem using the derivative formula
3.6.3. (p120) 2.6.3 Liouville theorem using the conformal change of metric
3.6.4. (p121) 2.6.4 Applications to harmonic maps and coupling Harmonic maps
3.7. (p123) 2.7 Notes
4. (p127) Chapter 3 Functional Inequalities and Essential Spectrum
4.1. (p127) 3.1 Essential spectrum on Hilbert spaces
4.1.1. (p127) 3.1.1 Functional inequalities
4.1.2. (p133) 3.1.2 Application to nonsymmetric semigroups
4.1.3. (p136) 3.1.3 Asymptotic kernels for compact operators
4.1.4. (p138) 3.1.4 Compact Markov operators without kernels
4.2. (p142) 3.2 Applications to coercive closed forms
4.3. (p145) 3.3 Super Poincaré inequalities
4.3.1. (p145) 3.3.1 The F-Sobolev inequality
4.3.2. (p150) 3.3.2 Estimates of semigroups
4.3.3. (p158) 3.3.3 Estimates of high order eigenvalues
4.3.4. (p160) 3.3.4 Concentration of measures for super Poincaré inequalities
4.4. (p163) 3.4 Criteria for super Poincaré inequalities
4.4.1. (p163) 3.4.1 A localization method
4.4.2. (p165) 3.4.2 Super Poincaré inequalities for jump processes
4.4.3. (p168) 3.4.3 Estimates of β for diffusion processes
4.4.4. (p173) 3.4.4 Some examples for estimates of high order eigenvalues
4.4.5. (p178) 3.4.5 Some criteria for diffusion processes
4.5. (p181) 3.5 Notes
5. (p182) Chapter 4 Weak Poicaré Inequalities and Convergence of Semigroups
5.1. (p182) 4.1 General results
5.2. (p189) 4.2 Concentration of measures
5.3. (p193) 4.3 Criteria of weak Poincaré inequalities
5.4. (p199) 4.4 Isoperimetric inequalities
5.4.1. (p199) 4.4.1 Diffusion processes on manifolds
5.4.2. (p203) 4.4.2 Jump processes
5.5. (p206) 4.5 Notes
6. (p208) Chapter 5 Log-Sobolev Inequalities and Semigroup Properties
6.1. (p208) 5.1 Three boundedness properties of semigroups
6.2. (p215) 5.2 Spectral gap for hyperbounded operators
6.3. (p225) 5.3 Concentration of measures for log-Sobolev inequalities
6.4. (p229) 5.4 Logarithmic Sobolev inequalities for jump processes
6.4.1. (p229) 5.4.1 Isoperimetric inequalities
6.4.2. (p231) 5.4.2 Criteria for birth-death processes
6.5. (p234) 5.5 Logarithmic Sobolev inequalities for one-dimensional diffusion processes
6.6. (p236) 5.6 Estimates of the log-Sobolev constant on manifolds
6.6.1. (p236) 5.6.1 Equivalent statements for the curvature condition
6.6.2. (p241) 5.6.2 Estimates of α(V) using Bakry-Emery s criterion
6.6.3. (p244) 5.6.3 Estimates of α(V) using Harnack inequality
6.6.4. (p250) 5.6.4 Estimates of α(V) using coupling
6.7. (p252) 5.7 Criteria of hypercontractivity, superboundedness and ultraboundedness
6.7.1. (p252) 5.7.1 Some criteria
6.7.2. (p262) 5.7.2 Ultraboundedness by perturbations
6.7.3. (p267) 5.7.3 Isoperimetric inequalities
6.7.4. (p270) 5.7.4 Some examples
6.8. (p271) 5.8 Strong ergodicity and log-Sobolev inequality
6.9. (p276) 5.9 Notes
7. (p279) Chapter 6 Interpolations of Poincaré and Log-Sobolev Inequalities
7.1. (p280) 6.1 Some properties of(6.0.3)
7.2. (p285) 6.2 Some criteria of(6.0.3)
7.3. (p291) 6.3 Transportation cost inequalities
7.3.1. (p293) 6.3.1 Otto-Villani s coupling
7.3.2. (p295) 6.3.2 Transportation cost inequalities
7.3.3. (p300) 6.3.3 Some results on (Ip)
7.4. (p304) 6.4 Notes
8. (p306) Chapter 7 Some Infinite Dimensional Models
8.1. (p306) 7.1 The(weighted)Poisson spaces
8.1.1. (p306) 7.1.1 Weak Poincaré inequalities for second quantization Dirichlet forms
8.1.2. (p309) 7.1.2 A class of jump processes on configuration spaces
8.1.3. (p314) 7.1.3 Functional inequalities for ？
8.2. (p317) 7.2 Analysis on path spaces over Riemannian manifolds
8.2.1. (p317) 7.2.1 Weak Poincaré inequality on finite-time interval path spaces
8.2.2. (p327) 7.2.2 Weak Poincaré inequality on infinite-time interval path spaces
8.2.3. (p331) 7.2.3 Transportation cost inequality on path spaces with L2-distance
8.2.4. (p339) 7.2.4 Transportation cost inequality on path spaces with the intrinsic distance
8.3. (p341) 7.3 Functional and Harnack inequalities for generalized Mehler semigroups
8.3.1. (p343) 7.3.1 Some general results
8.3.2. (p355) 7.3.2 Some examples
8.3.3. (p361) 7.3.3 A generalized Mehler semigroup associated with the Dirichlet heat semigroup
8.4. (p362) 7.4 Notes

Type: modern

In this book, the functional inequalities are introduced to describe:<br>(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;<br>(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;<br>(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.

Introducing the functional inequalities, this book describes: the spectrum of the generator, including the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap; the semigroup properties; and, the reference measure and the intrinsic metric.

本书的主要内容涉及概率论, 泛函分析, 微分几何和统计物理等多个学科, 较系统地介绍了近10年有关泛函不等式及其近10年来的有关泛函不等式及其应用的主要研究成果和研究方法.其中的一些成果和研究思想被国际同行专家大量引用, 引发了一系列的后续工作.以泛函不等式为主要工具研究马氏半群及其生成元的分析与概率性质

2024-06-13