| 王风雨，博士，1966年12月生于安徽省嘉山县。北京师范大学教授，长江学者特聘教授，博士生导师，国家杰出青年科学基金获得者。 曾应邀访问英国Warwick大学，还应邀访问过美国、法国、德国、俄罗斯、日本、新加坡、意大利和台湾等国家和地区的20余所大学和研究所，并多次在国际学术会议上作邀请报告。目前，担任中国概率统计学会常务理事，美国《数学评论》和德国《数学文摘》评论员，《应用概率统计》等杂志的编委。曾经作为洪堡学者在德国Bidefeld大学工作。 曾经获得钟嘉庆数学奖，教育部科技进步奖一.. << 查看详细 |
| contents chapter 0 preliminaries 0.1 dirichlet forms, sub-markov semigroups and generators 0.2 dirichlet forms and markov processes 0.3 spectral theory 0.4 riemannian geometry chapter 1 poincare inequality and spectral gap 1.1 a general result and examples 1.2 concentration of measures 1.3 poincare inequalities for jump processes 1.3.1 the bounded jump case 1.3.2 the unbounded jump case 1.3.3 a criterion for birth-death processes 1.4 poincare inequality for diffusion processes 1.4.1 the one-dimensional case 1.4.2 spectral gap for diffusion processes on rd 1.4.3 existence of the spectral gap on manifolds and application to nonsymmetric elliptic operators 1.5 notes chapter 2 diffusion processes on manifolds and applications 2.1 kendall-cranston's coupling .2.2 estimates of the first (closed and neumann) eigenvalue 2.3 estimates of the first two dirichlet eigenvalues 2.3.1 estimates of the first dirichlet eigenvalue 2.3.2 estimates of the second dirichlet eigenvalue and the spectral gap 2.4 gradient estimates of diffusion semigroups 2.4.1 gradient estimates of the closed and neumann semigroups 2.4.2 gradient estimates of dirichlet semigroups 2.5 harnack and isoperimetric inequalities using gradient estimates . 2.5.1 gradient estimates and the dimension-free harnack inequality 2.5.2 the first eigenvalue and isoperimetric constants 2.6 liouville theorems and couplings on manifolds 2.6.1 liouville theorem using the brownian radial process 2.6.2 liouville theorem using the derivative formula 2.6.3 liouville theorem using the conformal change of metric 2.6.4 applications to harmonic maps and coupling harmonic maps 2.7 notes chapter 3 functional inequalities and essential spectrum 3.1 essential spectrum on hilbert spaces 3.1.1 functional inequalities 3.1.2 application to nonsymmetric semigroups 3.1.3 asymptotic kernels for compact operators 3.1.4 compact markov operators without kernels 3.2 applications to coercive closed forms 3.3 super poincare inequalities 3.3.1 the f-sobolev inequality 3.3.2 estimates of semigroups 3.3.3 estimates of high order eigenvalues 3.3.4 concentration of measures for super poincare inequalities . 3.4 criteria for super poincare inequalities 3.4.1 a localization method 3.4.2 super poincare inequalities for jump processes 3.4.3 estimates of β for diffusion processes 3.4.4 some examples for estimates of high order eigenvalues 3.4.5 some criteria for diffusion processes 3.5 notes chapter 4 weak poincare inequalities and convergence of semigroups 4.1 general results 4.2 concentration of measures 4.3 criteria of weak poineare inequalities 4.4 isoperimetric inequalities 4.4.1 diffusion processes on manifolds 4.4.2 jump processes 4.5 notes chapter 5 log-sobolev inequalities and semigroup properties 5.1 three boundedness properties of semigroups 5.2 spectral gap for hyperbounded operators 5.3 concentration of measures for log-sobolev inequalities 5.4 logarithmic sobolev inequalities for jump processes 5.4.1 isoperimetric inequalities 5.4.2 criteria for birth-death processes 5.5 logarithmic sobolev inequalities for one-dimensional diffusion processes 5.6 estimates of the log-sobolev constant on manifolds 5.6.1 equivalent statements for the curvature condition 5.6.2 estimates of et(v) using bakry-emery's criterion 5.6.3 estimates of et(v) using harnack inequality 5.6.4 estimates of et(v) using coupling 5.7 criteria of hypercontractivity, superboundedness and ultraboundedness 5.7.1 some criteria 5.7.2 ultraboundedness by perturbations 5.7.3 lsoperimetric inequalities 5.7.4 some examples 5.8 strong ergodicity and log-sobolev inequality 5.9 notes chapter 6 interpolations of poincare and log-sobolev inequalities 6.1 some properties of (6.0.3) 6.2 some criteria of (6.0.3) 6.3 transportation cost inequalities 6.3.1 otto-villani's coupling 6.3.2 transportation cost inequalities 6.3.3 some results on (ip) 6.4 notes chapter 7 some infinite dimensional models 7.1 the (weighted) poisson spaces 7.1.1 weak poincare inequalities for second quantization dirichlet forms 7.1.2 a class of jump processes on configuration spaces 7.1.3 functional inequalities for 7.2 analysis on path spaces over riemannian manifolds 7.2.1 weak poincare inequality on finite-time interval path spaces 7.2.2 weak poincare inequality on infinite-time interval path spaces 7.2.3 transportation cost inequality on path spaces with l2-distance 7.2.4 transportation cost inequality on path spaces with the intrinsic distance 7.3 functional and harnack inequalities for generalized mehler semigroups 7.3.1 some general results 7.3.2 some examples 7.3.3 a generalized mehler semigroup associated with the dirichlet heat semigroup 7.4 notes bibliography index |
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