上海大学核心数学研究所——几何与分析综合报告第10讲 Functional Intrinsic Volumes

创建时间:  2022/06/29  龚惠英   浏览次数:   返回

报告题目 (Title):Functional Intrinsic Volumes

报告人 (Speaker): Monika Ludwig 教授(Technische Universität Wien)

报告时间 (Time):2022年6月29日(周三) 15:00-16:00

报告地点 (Place):Zoom meeting: 96210755509; 密码: SHU220629

邀请人(Inviter):席东盟、李晋、张德凯

主办部门:理学院数学系

报告摘要:A functional Z defined on a space of real-valued functions F is called a valuation if

for all such that , , . Here is the pointwise maximum of f and g, while is their pointwise minimum. The important,classical notion of valuations on convex bodies is a special case of the rather recent notion of valuations on function spaces.

We present a complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on Rn. This result corresponds to Hadwiger's celebrated theorem on the classification of continuous, translation and rotation invariant valuations on the space of convex bodies. The valuations obtained in our theorem are functional versions of the classical intrinsic volumes. Representations and important properties will be described.

(Based on joint work with Andrea Colesanti and Fabian Mussnig)

上一条:数学学科Seminar第2261讲 非交换极大不等式

下一条:数学学科Seminar第2259讲 Heavenly方程的对称性、分解和叠加


上海大学核心数学研究所——几何与分析综合报告第10讲 Functional Intrinsic Volumes

创建时间:  2022/06/29  龚惠英   浏览次数:   返回

报告题目 (Title):Functional Intrinsic Volumes

报告人 (Speaker): Monika Ludwig 教授(Technische Universität Wien)

报告时间 (Time):2022年6月29日(周三) 15:00-16:00

报告地点 (Place):Zoom meeting: 96210755509; 密码: SHU220629

邀请人(Inviter):席东盟、李晋、张德凯

主办部门:理学院数学系

报告摘要:A functional Z defined on a space of real-valued functions F is called a valuation if

for all such that , , . Here is the pointwise maximum of f and g, while is their pointwise minimum. The important,classical notion of valuations on convex bodies is a special case of the rather recent notion of valuations on function spaces.

We present a complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on Rn. This result corresponds to Hadwiger's celebrated theorem on the classification of continuous, translation and rotation invariant valuations on the space of convex bodies. The valuations obtained in our theorem are functional versions of the classical intrinsic volumes. Representations and important properties will be described.

(Based on joint work with Andrea Colesanti and Fabian Mussnig)

上一条:数学学科Seminar第2261讲 非交换极大不等式

下一条:数学学科Seminar第2259讲 Heavenly方程的对称性、分解和叠加