泛函不等式及其应用

摘要

This paper surveys some new progress concerning functional inequalitiesand applications to the study of Markov processes and spectral theory. We first briefly recallwe introduce functional inequalities to study the essential spectrum, the decay of Markovsemigroups, and the transportation cost inequalities.%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Poincaré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.