中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：焦勇教授（中南大学）
题 目：Noncommutative logarithmic Sobolev inequalities
时 间：2024.05.12（星期日）16:30-17:30
地 点：数学院南楼N818
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.
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