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The linear polarization constant of Rn

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He present work deals with estimations of the n-th linear polarization constant c(H)n of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup║y║=1 │<x1,y> ... <xn,y>│, where x1, ... ,xn are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) n= nn/2 remains open.

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  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O.B. 127, H-1364 Budapest

    Máté Matolcsi

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  1. Máté Matolcsi
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Matolcsi, M. The linear polarization constant of Rn. Acta Math Hung 108, 129–136 (2005). https://doi.org/10.1007/s10474-005-0214-y

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  • DOI: https://doi.org/10.1007/s10474-005-0214-y

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