Theoretical analysis establishes a complete classification of invariant valuations on convex functions, revealing functional counterparts to classical intrinsic volumes.
A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on Rⁿ 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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Colesanti et al. (2024) studied this question.
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