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
报告摘要：A functional Z defined on a space of real-valued functions F is called a valuation if
Z(f V g) + Z(f 𝞚g) = Z(f) + Z(g)
for all f,g in F such that f,g, f V g, f𝞚g in F. Heref V g is the pointwise maximum of f and g, whilef𝞚g 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)