Irreducible representations of deformed oscillator algebra and q-special functions

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.

Contribution to the workshop IWCQIS-96 (JINR, Dubna)

References in corpus (3)

• Special functions and q-commuting variables
• On the Two q-Analogue Logarithmic Functions
• Quantum Groups,Deformed Oscillators and their Interrelations

Cited by in corpus (2)

• On position operator spectral measure for deformed oscillator in the case of indetermine Hamburger moment problem
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish