A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912400131751936 |
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| author | Knoerr, Jonas |
| author_facet | Knoerr, Jonas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions Knoerr, Jonas Functional Analysis Metric Geometry 52B45, 26B25, 53C65, 52A39, 13P10 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. |
| title | A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions |
| topic | Functional Analysis Metric Geometry 52B45, 26B25, 53C65, 52A39, 13P10 |
| url | https://arxiv.org/abs/2505.22464 |