Functional inequalities, Markov semigroups and spectral theory / Feng-Yu Wang.

Format:

Book

Author/Creator:

Wang, Feng-Yu.

Series:

The Science Series of the Contemporary Elite Youth

Dang dai jie chu qing nian ke xue wen ku

Language:

English

Subjects (All):

Inequalities (Mathematics).

Semigroups.

Markov processes.

Spectral theory (Mathematics).

Physical Description:

1 online resource (391 p.)

Other Title:

Functional inequatities, [sic] Markov semigroups and spectral theory

Fan han bu deng shi, Ma'erkefu ban qun yu pu li lun

Place of Publication:

Beijing ; New York : Science press, c2005.

Language Note:

English

Summary:

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.

Contents:

Front Cover; Functional Inequalities, Markov Semigroups and Spectral Theory; Copyright Page; 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; 1.4 Poincaré inequality for diffusion processes; 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) eigenvalue2.3 Estimates of the first two Dirichlet eigenvalues; 2.4 Gradient estimates of diffusion semigroups; 2.5 Harnack and isoperimetric inequalities using gradient estimates; 2.6 Liouville theorems and couplings on manifolds; 2.7 Notes; Chapter 3. Functional Inequalities and Essential Spectrum; 3.1 Essential spectrum on Hilbert spaces; 3.2 Applications to coercive closed forms; 3.3 Super Poincaré inequalities; 3.4 Criteria for super Poincaré inequalities; 3.5 Notes; Chapter 4. Weak Poincaré Inequalities and Convergence of Semigroups

4.1 General results4.2 Concentration of measures; 4.3 Criteria of weak Poincaré inequalities; 4.4 Isoperimetric inequalities; 4.5 Notes; Chapter 5. Log-Sobolev Inequalities and Semigroup Properties; 5.1 Three boundedness properties of semigroups; 5.2 Spectral gap for hyperbounded operators .; 5.3 Concentration of measures for log-Sobolev inequalities; 5.4 Logarithmic Sobolev inequalities for jump processes; 5.5 Logarithmic Sobolev inequalities for one-dimensional diffusion processes; 5.6 Estimates of the log-Sobolev constant on manifolds

5.7 Criteria of hypercontractivity, superboundedness and ultraboundedness5.8 Strong ergodicity and log-Sobolev inequality; 5.9 Notes; Chapter 6. Interpolations of Poincaré and Log-Sobolev Inequalities; 6.1 Some properties of (6.0.3); 6.2 Some criteria of (6.0.3); 6.3 Transportation cost inequalities; 6.4 Notes; Chapter 7. Some Infinite Dimensional Models; 7.1 The (weighted) Poisson spaces; 7.2 Analysis on path spaces over Riemannian manifolds; 7.3 Functional and Harnack inequalities for generalized Mehler semigroups; 7.4 Notes; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-281-14468-1

9786611144685

0-08-053207-1

OCLC:

476128472