On the $n-$th linear polarization constant of $\mathbb{R}^n$

Autor:	Pinasco, Damian
Rok vydání:	2022
Předmět:	Mathematics - Functional Analysis Primary 46G25 Secondary 26D05 52A40
Druh dokumentu:	Working Paper
Popis:	We prove that given any set of $n$ unit vectors $\{v_i\}_{i=1}^{n}\subset \mathbb R^n,$ the inequality \[ \sup\limits_{\Vert x \Vert_{\mathbb R^n} =1} \vert \langle x, v_1 \rangle \cdots \langle x, v_n\rangle\vert \ge n^{-n/2} \] holds for $n \le 14.$ Moreover, the equality is attained if and only if $\{v_i\}_{i=1}^{n}$ is an orthonormal system.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.05584 Zobrazit plný text záznamu View this record from Arxiv