On the $n-$th linear polarization constant of $\mathbb{R}^n$
Autor: | Pinasco, Damian |
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Rok vydání: | 2022 |
Předmět: | |
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 |
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