Generalized coherent states for $q$-oscillator connected with discrete $q$-Hermite polynomials
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 33, Tome 308 (2004), pp. 48-66
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We are continuing here the study of generalized coherent states of Barut–Girardello type for the oscillator-like systems connected with the given set of orthogonal polynomials. In this work we construct the family of coherent states associated with discrete $q$-Hermite polynomials of the II-type and prove the over-completeness of this family of states by constructing the measure for unity decomposition for this family of coherent states.
@article{ZNSL_2004_308_a3,
author = {V. V. Borzov and E. V. Damaskinsky},
title = {Generalized coherent states for $q$-oscillator connected with discrete $q${-Hermite} polynomials},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {48--66},
publisher = {mathdoc},
volume = {308},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_308_a3/}
}
TY - JOUR AU - V. V. Borzov AU - E. V. Damaskinsky TI - Generalized coherent states for $q$-oscillator connected with discrete $q$-Hermite polynomials JO - Zapiski Nauchnykh Seminarov POMI PY - 2004 SP - 48 EP - 66 VL - 308 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2004_308_a3/ LA - ru ID - ZNSL_2004_308_a3 ER -
%0 Journal Article %A V. V. Borzov %A E. V. Damaskinsky %T Generalized coherent states for $q$-oscillator connected with discrete $q$-Hermite polynomials %J Zapiski Nauchnykh Seminarov POMI %D 2004 %P 48-66 %V 308 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2004_308_a3/ %G ru %F ZNSL_2004_308_a3
V. V. Borzov; E. V. Damaskinsky. Generalized coherent states for $q$-oscillator connected with discrete $q$-Hermite polynomials. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 33, Tome 308 (2004), pp. 48-66. http://geodesic.mathdoc.fr/item/ZNSL_2004_308_a3/