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Finite tight frames and some applications
Cotfas N., Gazeau J.-P.
Journal of Physics A: Mathematical and Theoretical 43 (2010) 193001 - http://hal.in2p3.fr/in2p3-00353252
Mathématiques/Physique mathématique
Physique/Physique mathématique
Finite tight frames and some applications
N. Cotfas, J.-P. Gazeau1
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
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.

Articles dans des revues avec comité de lecture
Journal of Physics A: Mathematical and Theoretical
Publisher Institute of Physics: Hybrid Open Access
ISSN 1751-8113 (eISSN : 1751-8121)

Mathematical physics – Computational physics – Quantum information and quantum mechanics
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