UID:
almahu_9947365842302882
Format:
1 online resource (391 p.)
ISBN:
1-281-14468-1
,
9786611144685
,
0-08-053207-1
Series Statement:
Dang dai jie chu qing nian ke xue wen ku
Content:
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.
Note:
Description based upon print version of record.
,
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
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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
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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
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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
,
English
Additional Edition:
ISBN 0-08-044942-5
Language:
English
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