Functional inequalities, Markov semigroups and spectral theory.
Collection : Dang dai jie chu qing nian ke xue wen ku Détails physiques : 1 online resource. ISBN :9780080449425; 0080449425.
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Semigroups.
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Markov processes.
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Spectral theory (Mathematics)
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Functional analysis.
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Electronic books.
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Inequalities (Mathematics)
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Markov processes.
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Semigroups.
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Spectral theory (Mathematics)
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.
Chapter 0: Preliminaries -- Chapter 1 Poinc̀re 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 .
Includes bibliographical references and index.
Description based on print version record.
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