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- Title
Monge–Ampère operators and valuations.
- Authors
Knoerr, Jonas
- Abstract
Two classes of measure-valued valuations on convex functions related to Monge–Ampère operators are investigated and classified. It is shown that the space of all valuations with values in the space of complex Radon measures on R n that are locally determined, continuous, dually epi-translation invariant as well as translation equivariant, is finite dimensional. Integral representations of these valuations and a description in terms of mixed Monge–Ampère operators are established, as well as a characterization of SO (n) -equivariant valuations in terms of Hessian measures.
- Subjects
VALUATION; INTEGRAL representations; CONVEX functions; RADON
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 4, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-024-02698-5