The Hadwiger Theorem on Convex Functions, I

By Andrea Colesanti, Monika Ludwig, F. Mussnig. Geometric and Functional Analysis, 2020

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A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb{R}}^{n}$\end{document} is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.

Subfields: Applied Mathematics, Mathematical Physics

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