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

Text
0611947v1.pdf Restricted to Repository staff only Download (112kB) | Request a copy |

## 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 |
---|---|

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 |

### Actions (login required)

Edit Item |