The Hadwiger theorem on convex functions, I

Abstract

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.

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Cited by in corpus (6)

• Additive kinematic formulas for convex functions
• Metrics and Isometries for Convex Functions
• A Riesz representation theorem for log-concave functions
• A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions
• Inequalities and counterexamples for functional intrinsic volumes and beyond
• The Legendre transform, the Laplace transform and valuations