Polynomial local functionals on convex functions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908718184005632 |
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| author | Knoerr, Jonas |
| author_facet | Knoerr, Jonas |
| contents | We shown that every continuous local functional on the space of finite convex functions on $\mathbb{R}^n$ is a valuation. This relation is used to establish a homogeneous decomposition for the class of polynomial local functionals as well as a classification of translation or rigid motion invariant polynomial local functionals. In addition we discuss implications for the compact-open topology on the space of polynomial local functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial local functionals on convex functions Knoerr, Jonas Functional Analysis 52B45, 26B25, 47H60, 53C65 We shown that every continuous local functional on the space of finite convex functions on $\mathbb{R}^n$ is a valuation. This relation is used to establish a homogeneous decomposition for the class of polynomial local functionals as well as a classification of translation or rigid motion invariant polynomial local functionals. In addition we discuss implications for the compact-open topology on the space of polynomial local functionals. |
| title | Polynomial local functionals on convex functions |
| topic | Functional Analysis 52B45, 26B25, 47H60, 53C65 |
| url | https://arxiv.org/abs/2512.15402 |