Year: 2025
Type: preprint
Abstract: 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 $p \geq 6.8$.
Source: arXiv (Cornell University)
Author: Instanes, Sarah May
Institution: Norwegian University of Science and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083843764
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