Carlson's theorem and vertical limit functions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912632693325824 |
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| author | Brevig, Ole Fredrik Kouroupis, Athanasios |
| author_facet | Brevig, Ole Fredrik Kouroupis, Athanasios |
| contents | We extend a classical theorem of Carlson on moments of Dirichlet series from $p=2$ to $1 \leq p < \infty$. When combined with the ergodic theorem for the Kronecker flow, a coherent approach to almost sure properties of vertical limit functions in $H^p$ spaces of Dirichlet series is obtained. This allows us to establish an almost sure analytic continuation of vertical limit functions to the right half-plane that can be used to compute the $H^p$ norm and to prove a version of Fatou's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05793 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carlson's theorem and vertical limit functions Brevig, Ole Fredrik Kouroupis, Athanasios Classical Analysis and ODEs Functional Analysis We extend a classical theorem of Carlson on moments of Dirichlet series from $p=2$ to $1 \leq p < \infty$. When combined with the ergodic theorem for the Kronecker flow, a coherent approach to almost sure properties of vertical limit functions in $H^p$ spaces of Dirichlet series is obtained. This allows us to establish an almost sure analytic continuation of vertical limit functions to the right half-plane that can be used to compute the $H^p$ norm and to prove a version of Fatou's theorem. |
| title | Carlson's theorem and vertical limit functions |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2510.05793 |