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Irreducible representations of deformed oscillator algebra and q-special functions

E. V. Damaskinsky·P. P. Kulish
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Abstract

Different generators of a deformed oscillator algebra give rise to one-parameter families of $q$-exponential functions and $q$-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment problems with the corresponding resolution of unity for the $q$-coherent states and with 'coordinate' operators - Jacobi matrices, are also pointed out.

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E. V. Damaskinsky, P. P. Kulish. 1996-10-01. Irreducible representations of deformed oscillator algebra and q-special functions. https://doi.org/10.1142/s0217751x97000207

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