论文标题
在$ n- $ th的线性极化常数$ \ mathbb {r}^n $上
On the $n-$th linear polarization constant of $\mathbb{R}^n$
论文作者
论文摘要
我们证明，给定任何集合$ n $单位向量$ \ {v_i \} _ {i = 1}^{n}^{n} \ subset \ subbb r^n，$ the no不平等\ [\ sup \ sup \ limits _ { \ rangle \ cdots \ langle x，v_n \ rangle \ vert \ ge n^{ - n/2} \]持有$ n \ le 14. $。此外，当且仅在$ \ {v_i \} _ = 1} _ = 1}^n} $或一个系统时，仅在且仅在$ \ {v_i \}时实现等值。
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.
