arXiv:0803.0077 · Journal of Physics A Mathematical and Theoretical

Finite tight frames and some applications

Nicolae Cotfas, Jean‐Pierre Gazeau

Published Apr 20, 2010• 41 citations

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.

DOI: 10.1088/1751-8113/43/19/193001

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