On the n−th linear polarization constant of Rn
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Mathematische Nachrichten
Abstract
Abstract. We prove that given any set of n unit vectors {vi}n
i=1 ⊂ Rn, the
inequality
sup
kxkRn=1
|hx, v1i · · · hx, vni| ≥ n−n/2
holds for n ≤ 14. Moreover, the equality is attained if and only if {vi}n
i=1 is
an orthonormal system.
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Keywords
Matemáticas, Linear polarization constants, Product of linear functionals