Matolcsi, Máté (2005) A geometric estimate on the norm of product of functionals. LINEAR ALGEBRA AND ITS APPLICATIONS, 405. pp. 304-310. ISSN 0024-3795
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Abstract
The open problem of determining the exact value of the n-th linear polarization constant cn of Rn has received considerable attention over the past few years. This paper makes a contribution to the subject by providing a new lower bound on the value of supkyk=1 | hx1, yi · · · hxn, yi |, where x1, . . . , xn are unit vectors in Rn. The new estimate is given in terms of the eigenvalues of the Gram matrix [hxi, xji] and improves upon earlier estimates of this kind. However, the intriguing conjecture cn = n n/2 remains open.
Item Type: | Article |
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Uncontrolled Keywords: | Functions; VECTORS; Theorem proving; Polynomials; POLARIZATION; Matrix algebra; GEOMETRY; eigenvalues and eigenfunctions; Product of functionals; Polynomials over normed spaces; Linear polarization constants; Gram matrices; SPACES; CONSTANTS; Plank problem; linear polarization constants |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 10 Dec 2013 14:06 |
Last Modified: | 10 Dec 2013 14:06 |
URI: | http://real.mtak.hu/id/eprint/7955 |
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