A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.
The Hadwiger Theorem on Convex Functions, I / Colesanti, Andrea; Ludwig, Monika; Mussnig, Fabian. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - ELETTRONICO. - (2024), pp. 1-60. [10.1007/s00039-024-00693-8]
The Hadwiger Theorem on Convex Functions, I
Colesanti, Andrea;Mussnig, Fabian
2024
Abstract
A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions 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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