Functional inequalities, Markov semigroups and spectral theory
Title:
Functional inequalities, Markov semigroups and spectral theory
Author:
Wang, Feng-Yu.
ISBN:
9780080449425
Personal Author:
Publication Information:
Beijing ; New York : Science Press, c2005
Physical Description:
p. cm.
Contents:
Chapter 0: Preliminaries -- -- Chapter 1 Poinácre Inequality and Spectral Gap -- -- Chapter 2 Diffusion Processes on Manifolds and Applications -- -- Chapter 3 Functional Inequalities and Essential Spectrum -- -- Chapter 4: Weak Poincare Inequalities and Convergence of Semigroups -- Chapter 5 Log-Sobolev Inequalities and Semigroup Properties -- -- Chapter 6 Interpolations of Poincare and Log-Sobolev Inequalities -- -- Chapter 7 Some Infinite Dimensional Models -- -- Bibliography -- -- Index<P>.
Abstract:
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.
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