报告题目 (Title)：Noncommutative logarithmic Sobolev inequalities
中文标题：非交換的對數Sobolev不等式
报告人 (Speaker)：焦勇 教授（中南大学）
报告时间 (Time)：2024年4月10日(周三) 10:00
报告地点 (Place)：腾讯会议（514-885-492）
邀請人(Inviter)：席東盟、李晉、張德凱、吳加勇
主办部門：理學院数学系
报告摘要：We show that the logarithmic Sobolev inequality holds for an arbitrary hypercontractive semigroup acting on a noncommutative probability space. Particularly, we can recover the p-logarithmic Sobolev inequality whenever the Riesz transform is bounded. Our inequality applies to numerous concrete cases, including Poisson semigroups for free groups, the Ornstein-Uhlenbeck semigroup for mixed Q-gaussian von Neumann algebras, the free product for Ornstein-Uhlenbeck semigroups etc. This provides a unified abstract approach to logarithmic Sobolev inequalities in noncommutative setting.
