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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.24485 |
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| _version_ | 1866913065492021248 |
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| author | Knoerr, Jonas |
| author_facet | Knoerr, Jonas |
| contents | Integral representations for continuous polynomial local functionals on convex functions are established in terms of a finite family of polynomials. This result is obtained by approximation from a classification of the dense subspace of smooth polynomial local functionals, which is based on a Paley--Wiener--Schwartz-type classification of the Goodey--Weil distributions associated to these functionals under support restrictions. As an application, density results for various families of Monge--Ampère-type operators are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24485 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integral representation of polynomial local functionals on convex functions Knoerr, Jonas Functional Analysis 52B45, 26B25, 47H60 Integral representations for continuous polynomial local functionals on convex functions are established in terms of a finite family of polynomials. This result is obtained by approximation from a classification of the dense subspace of smooth polynomial local functionals, which is based on a Paley--Wiener--Schwartz-type classification of the Goodey--Weil distributions associated to these functionals under support restrictions. As an application, density results for various families of Monge--Ampère-type operators are established. |
| title | Integral representation of polynomial local functionals on convex functions |
| topic | Functional Analysis 52B45, 26B25, 47H60 |
| url | https://arxiv.org/abs/2604.24485 |