Linear polarization constant of ${\mathbb{R}}^n$

Abstract

The present work contributes to the determination of the $n$-th linear polarization constant $c_n(H)$ of an $n$-dimensional real Hilbert space $H$. We provide some new lower bounds on the value of ${\sup }_{\Vert y\Vert =1}|x_1,y>...x_n,y|$, where $x_1,...,x_n$ are unit vectors in $H$. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture $c_n(H)=n^{n/2}$ remains open.

8 pages

References in corpus (1)

• The plank problem for symmetric bodies

Cited by in corpus (1)

• Inequalities for Multivariate Polynomials