Generalized Coherent States for the q-Oscillator Associated with Discrete q-Hermite Polynomials

We continue studying generalized coherent states of the Barut-Girardello type for oscillator-like systems related to a given set of orthogonal polynomials. In this paper we construct a family of coherent states associated with discrete q-Hermite polynomials of the II-type and prove the overcompleteness of this family by constructing the measure in the unity decomposition for this family of coherent states. Bibliography: 49 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 48–66.