On the n−th linear polarization constant of Rn

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Mathematische Nachrichten

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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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Matemáticas, Linear polarization constants, Product of linear functionals

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