The d-th linear polarization constant of R
نویسندگان
چکیده
In [4] it was conjectured that for all unit vectors u1, · · · , ud in Rd, X (u1, · · · , ud) := sup x∈Rd, |x|2=d d ∏ i=1 〈x, ui〉 ≥ 1 with equality occurring iff u1, · · · , ud are orthonormal. We relate this to a conjecture about solutions of Ay = y−1, where A = (〈ui, uj〉), and show that if the conjecture fails then the u1, · · · , ud minimizing X must be linearly dependent. We also show X (u1, · · · , ud) ≥ 1 for certain families of u1, · · · , ud.
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تاریخ انتشار 2008