Volume 27, pp. 140-155, 2007.

An algebra of integral operators

Sergei K. Suslov

Abstract

We introduce an algebra of integral operators related to a model of the $q$-harmonic oscillator and investigate some of its properties.

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Key words

integral operators, divided difference operators, the continuous $q$-Hermite polynomials, generating functions, Poisson kernel, bilinear generating functions, $q$-harmonic oscillators

AMS subject classifications

%Primary 33D45, 42C10; Secondary 45E10 33D45, 42C10, 45E10