Feng-Yu W. Functional Inequalities Markov Semigroups and Spectral Theory

Elsevier Science, 2006. — 390 p.n 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.Preliminaries
Poincaré Inequality and Spectral Gap
Diffusion Processes on Manifolds and Applications
Functional Inequalities and Essential Spectrum
Weak Poincaré Inequalities and Convergence of Semigroups
Log-Sobolev Inequalities and Semigroup Properties
Interpolations of Poincaré and Log-Sobolev Inequalities
Some Infinite Dimensional Models
Bibliography
Index