Functional Inequalities Markov Semigroups and Spectral Theory book cover

Functional Inequalities Markov Semigroups and Spectral Theory

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.

mathematicians, libraries, departments of mathematics


Published: February 2006

Imprint: Elsevier

ISBN: 978-0-08-044942-5


  • 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


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