Point evaluation for polynomials on the circle
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917489660657664 |
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| author | Instanes, Sarah May |
| author_facet | Instanes, Sarah May |
| contents | We study the constant $\mathscr{C}_{d,p}$ defined as the smallest constant $C$ such that $\|P\|_\infty^p \leq C\|P\|_p^p$ holds for every polynomial $P$ of degree $d$, where we consider the $L^p$ norm on the unit circle. We conjecture that $\mathscr{C}_{d,p} \leq dp/2+1$ for all $p \geq 2$ and all degrees $d$. We show that the conjecture holds for all $p \geq 2$ when $d \leq 4$ and for all $d$ when $p \geq 6.8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Point evaluation for polynomials on the circle Instanes, Sarah May Complex Variables 42A05 (primary), 26D05 (secondary) We study the constant $\mathscr{C}_{d,p}$ defined as the smallest constant $C$ such that $\|P\|_\infty^p \leq C\|P\|_p^p$ holds for every polynomial $P$ of degree $d$, where we consider the $L^p$ norm on the unit circle. We conjecture that $\mathscr{C}_{d,p} \leq dp/2+1$ for all $p \geq 2$ and all degrees $d$. We show that the conjecture holds for all $p \geq 2$ when $d \leq 4$ and for all $d$ when $p \geq 6.8$. |
| title | Point evaluation for polynomials on the circle |
| topic | Complex Variables 42A05 (primary), 26D05 (secondary) |
| url | https://arxiv.org/abs/2509.22035 |