The Hadwiger Theorem on Convex Functions, I

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2024年10月16日

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Andrea Colesanti,
Monika Ludwig,
Fabian Mussnig

摘要

A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb{R}}^{n}$ is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.