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Finite tight frames and some applications

N. Cotfas J.-P. Gazeau 1
1 APC - THEORIE
APC (UMR_7164) - AstroParticule et Cosmologie, Institut für theoretische Physik
Abstract : 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.
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Submitted on : Thursday, January 15, 2009 - 11:01:34 AM
Last modification on : Wednesday, October 21, 2020 - 4:32:14 PM

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N. Cotfas, J.-P. Gazeau. Finite tight frames and some applications. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43, pp.193001. ⟨10.1088/1751-8113/43/19/193001⟩. ⟨in2p3-00353252⟩

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