| 泛函不等式及其应用 |
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| 引用本文： | 王凤雨. 泛函不等式及其应用[J]. 数学进展, 2003, 32(5): 513-528 |
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| 作者姓名： | 王凤雨 |
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| 作者单位： | 北京师范大学数学系,北京,100875,中国 |
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| 基金项目： | Research supported in part by NSFC(No. 10121101, No. 10025105), TRAPOYT and the 973-Project |
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| 摘 要： | 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Poincare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．
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| 关 键 词： | 泛函不等式 谱理论 马氏过程 Poincare不等式 对数不等式 马氏半群 本征谱 收敛速度 运费不等式 |
Functional Inequalities and Applications |
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| WANG Feng-yu. Functional Inequalities and Applications[J]. Advances in Mathematics(China), 2003, 32(5): 513-528 |
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| Authors: | WANG Feng-yu |
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| Abstract: | 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. |
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| Keywords: | functional inequality essential spectrum Markov semigroup transporta- tion cost inequality |
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