An optimization problem and point-evaluation in Paley-Wiener spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916406566584320 |
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| author | Instanes, Sarah May |
| author_facet | Instanes, Sarah May |
| contents | We study the constant $\mathscr{C}_p$ defined as the smallest constant $C$ such that $|f(0)|^p \leq C\|f\|_p^p$ holds for every function $f$ in the Paley-Wiener space $PW^p$. Brevig, Chirre, Ortega-Cerdà, and Seip have recently shown that $\mathscr{C}_p<p/2$ for all $p>2$. We improve this bound for $2<p \leq 5$ by solving an optimization problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_11963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An optimization problem and point-evaluation in Paley-Wiener spaces Instanes, Sarah May Classical Analysis and ODEs Complex Variables Functional Analysis 30D15 We study the constant $\mathscr{C}_p$ defined as the smallest constant $C$ such that $|f(0)|^p \leq C\|f\|_p^p$ holds for every function $f$ in the Paley-Wiener space $PW^p$. Brevig, Chirre, Ortega-Cerdà, and Seip have recently shown that $\mathscr{C}_p<p/2$ for all $p>2$. We improve this bound for $2<p \leq 5$ by solving an optimization problem. |
| title | An optimization problem and point-evaluation in Paley-Wiener spaces |
| topic | Classical Analysis and ODEs Complex Variables Functional Analysis 30D15 |
| url | https://arxiv.org/abs/2409.11963 |