A geometric decomposition for unitarily invariant valuations on convex functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911975302234112 |
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| author | Knoerr, Jonas |
| author_facet | Knoerr, Jonas |
| contents | Valuations on the space of finite-valued convex functions on $\mathbb{C}^n$ that are continuous, dually epi-translation invariant, as well as $\mathrm{U}(n)$-invariant are completely classified. It is shown that the space of these valuations decomposes into a direct sum of subspaces defined in terms of vanishing properties with respect to restrictions to a finite family of special subspaces of $\mathbb{C}^n$, mirroring the behavior of the hermitian intrinsic volumes introduced by Bernig and Fu. Unique representations of these valuations in terms of principal value integrals involving two families of Monge-Ampère-type operators are established |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A geometric decomposition for unitarily invariant valuations on convex functions Knoerr, Jonas Functional Analysis Differential Geometry Metric Geometry 52B45, 26B25, 53C65, 32W20 Valuations on the space of finite-valued convex functions on $\mathbb{C}^n$ that are continuous, dually epi-translation invariant, as well as $\mathrm{U}(n)$-invariant are completely classified. It is shown that the space of these valuations decomposes into a direct sum of subspaces defined in terms of vanishing properties with respect to restrictions to a finite family of special subspaces of $\mathbb{C}^n$, mirroring the behavior of the hermitian intrinsic volumes introduced by Bernig and Fu. Unique representations of these valuations in terms of principal value integrals involving two families of Monge-Ampère-type operators are established |
| title | A geometric decomposition for unitarily invariant valuations on convex functions |
| topic | Functional Analysis Differential Geometry Metric Geometry 52B45, 26B25, 53C65, 32W20 |
| url | https://arxiv.org/abs/2408.01352 |