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The Vectorial Hadwiger Theorem on Convex Functions
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A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally extend the classical Minkowski relations. For this, the existence of these operators with singular densities is shown, along with additional representations involving mixed Monge-Amp\`ere measures, Kubota-type formulas, and area measures of higher dimensional convex bodies. Dual results are formulated for valuations on super-coercive convex functions.
Forward citations
Cited by 2 Pith papers
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A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions
The paper proves a Paley-Wiener-Schwartz theorem for dually epi-translation invariant valuations on convex functions and uses it to classify all closed affine invariant subspaces.
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Polynomial local functionals on convex functions
Continuous local functionals on convex functions are valuations, yielding homogeneous decompositions and invariant classifications of polynomial local functionals.
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