On Steiner entire function
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915391819743232 |
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| author | Dospolova, Maria Germanskov, Mikhail Zaporozhets, Dmitry |
| author_facet | Dospolova, Maria Germanskov, Mikhail Zaporozhets, Dmitry |
| contents | We introduce and study the Steiner entire function, an analytic generating function for the intrinsic volumes of a convex compact set in a Hilbert space. This function extends the classical Steiner polynomial to infinite dimensions and encodes key geometric information about the set. We establish fundamental results on its order, type, and canonical product representation, and show how its analytic growth properties characterize Gaussian continuity. In particular, we provide new criteria for this property in terms of entire function theory, disprove a conjecture of Gao and Vitale, and conjecture a new characterization of admissible intrinsic volume sequences in infinite dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Steiner entire function Dospolova, Maria Germanskov, Mikhail Zaporozhets, Dmitry Metric Geometry Complex Variables Probability 52A05, 30D15, 60G15 We introduce and study the Steiner entire function, an analytic generating function for the intrinsic volumes of a convex compact set in a Hilbert space. This function extends the classical Steiner polynomial to infinite dimensions and encodes key geometric information about the set. We establish fundamental results on its order, type, and canonical product representation, and show how its analytic growth properties characterize Gaussian continuity. In particular, we provide new criteria for this property in terms of entire function theory, disprove a conjecture of Gao and Vitale, and conjecture a new characterization of admissible intrinsic volume sequences in infinite dimensions. |
| title | On Steiner entire function |
| topic | Metric Geometry Complex Variables Probability 52A05, 30D15, 60G15 |
| url | https://arxiv.org/abs/2507.11626 |