HAL : in2p3-00353252, version 1

arXiv : 0803.0077

DOI : 10.1088/1751-8113/43/19/193001

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Journal of Physics A: Mathematical and Theoretical 43 (2010) 193001

Finite tight frames and some applications

N. Cotfas, J.-P. Gazeau1

(2010)

A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer some advantages. The use of a finite tight frame may lead to a simpler description of the symmetry transformations, to a simpler and more symmetric form of invariants or to the possibility of defining new mathematical objects with physical meaning, particularly in regard with the notion of a quantization of a finite set. We present some results concerning the use of integer coefficients and frame quantization, and several examples, and suggest some possible applications.

1 :	APC - AstroParticule et Cosmologie

équipe(s) de recherche : APC - THEORIE

Thème(s)

:

Mathématiques/Physique mathématique Physique/Physique mathématique

Mot(s)-clé(s) : Mathematical physics – Computational physics – Quantum information and quantum mechanics

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Soumis le : Jeudi 15 Janvier 2009, 11:01:34

Dernière modification le : Lundi 25 Juin 2012, 18:43:13