Functional Inequalities, Markov Semigroups and Spectral Theory

Author: Wang Fengyu
Publisher:
Publish Date: 2005-01-01
Features: The main content of this book involves multiple disciplines such as probability theory, functional analysis, differential geometry, and statistical physics, systematically introducing the main research achievements and methods related to functional inequalities over the past decade. Some of these achievements and research ideas have been widely cited by international peers, triggering a series of follow-up works. The book primarily uses functional inequalities as tools to study the analytical and probabilistic properties of Markov semigroups and their generators. Specifically, it employs weak inequalities to characterize the convergence rates of Markov semigroups; uses super inequalities to describe the uniform integrability of semigroups, as well as the eigen spectra of generators and the estimation of higher eigenvalues; and introduces inequalities of general additivity to characterize exponential convergence of Markov semigroups under different senses and the upper bounds of probabilistic distances.