Probabilistic aspects of finite frame quantization
Nicolae Cotfas, Jean-Pierre Gazeau · arXiv (Cornell University) · 2008
Abstract. We present a version for finite groups of the construction of coherent states proposed by Perelomov in the case of Lie groups, and use it in order to define some finite frames directly related to certain crystals/quasicrystals. These frames allow us to associate to any complex valued function supported by the crystal/quasicrystal nodes a linear operator in a finite-dimensional space, whose spectrum and mean values may shed a new (possibly probabilistic) light on the geometrical structure. The procedure, not necessarily a path to a quantum approach, can be regarded as an extended version of the Klauder-Berezin quantization and represents a change of point of view in considering the crystal/quasicrystal. Probabilistic aspects of finite frame quantization 2 1.