Linear polarization constant of $\R^n$

Details Linear polarization constant of $\R^n$ Linear polarization constant of $\R^n$

2006-11-30

arxiv.org/abs/math/0611946v1

Acta Math. Hungar. 108 (2005), no. 1-2, 129--136

Mathematics

Classical Analysis and ODEs

8 pages

Scientific paper

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 $\sup_{\|y\|=1}| x_1,y >... x_n,y |$, 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.

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