泛函不等式及其应用(英文)

Functional Inequalities and Applications

本文介绍有关泛函不等式及谱理论与马氏过程研究的若干新进展.我们首先简要回顾了两个著名不等式,即Poincar不等式与对数不等式,然后分别使用泛函不等式研究本征谱、马氏半群的收敛速度和运费不等式.

This paper surveys some new progress concerning functional inequalities and applications to the study of Markov processes and spectral theory. We first briefly recall two well-known inequalities, i.e. the log-Sobolev inequality and Poincare inequality, then we introduce functional inequalities to study the essential spectrum, the decay of Markov semigroups, and the transportation cost inequalities.