A Paley–Wiener–Schwartz Theorem for Smooth Valuations on Convex Functions
Abstract
Abstract Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier–Laplace transform of the associated Goodey–Weil distributions. This description is used to obtain integral representations of the smooth vectors of the natural representation of the group of translations on the space of these valuations. As an application, a complete classification of all closed and affine invariant subspaces is established, yielding density results for valuations defined in terms of mixed Monge–Ampère operators.
Fields of Study & Subjects
Geometry and complex manifolds
Holomorphic and Operator Theory
Point processes and geometric inequalities
Publication details
- Journal / source
- Geometric and Functional Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 4
- Pages
- 1071–1130
- Publication date
- 1 August 2026
- Language
- EN