On the n-th polarization constant of R^n

Abstract

In this paper we prove that given any set of $n$ unit vectors ${v_i}_{i=1}^{n}subset zR^n,$ the inequality[suplimits_{Vert x Vert_{zR^n} =1} ert langle x, v_1 angle cdots langle x, v_nangleert 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.