Functional Inequalities Markov Semigroups and Spectral Theory


  • Fengyu Wang, School of Mathematical Sciences, Beijing Normal University

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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Book information

  • Published: February 2006
  • Imprint: ELSEVIER
  • ISBN: 978-0-08-044942-5

Table of Contents

Chapter 0: Preliminaries
Chapter 1 Poincáre 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 SemigroupsChapter 5 Log-Sobolev Inequalities and Semigroup Properties
Chapter 6 Interpolations of Poincare and Log-Sobolev Inequalities
Chapter 7 Some Infinite Dimensional Models