Finite tight frames and some applications

Details Finite tight frames and some applications Finite tight frames and some applications

2008-03-02

arxiv.org/abs/0803.0077v4

J. Phys.A: Math. Theor. 43 (2010) 193001 (26pp)

Physics

Mathematical Physics

28 pages, LaTeX in IOP style, New results added

Scientific paper

10.1088/1751-8113/43/19/193001

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 to define 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, several examples and suggest some possible applications.

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