The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree n are classified. By duality, corresponding results are obtained for valuations on finite-valued convex functions.
A homogeneous decomposition theorem for valuations on convex functions / Colesanti A.; Ludwig M.; Mussnig F.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - ELETTRONICO. - 279:(2020), pp. 1-25. [10.1016/j.jfa.2020.108573]
A homogeneous decomposition theorem for valuations on convex functions
Colesanti A.
;
2020
Abstract
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree n are classified. By duality, corresponding results are obtained for valuations on finite-valued convex functions.
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