A q-oscillator Green’s function

Abstract

By using the generating function formula for the product of two q-Hermite polynomials q-deformation of the Feynman Green function for the harmonic oscillator is obtained.

Green function on the quantum plane

“…In Section 2 we recall main result [2,3,4,5,6,7] concerning the quantum group E q (2) and its homogeneous spaces.…”

On the sufficient conditions of the localization of the Fourier-Laplace series of distributions from liouville classes

“…In the case of Spectral expansions of the integrable functions on unit sphere the same problems are considered in the papers [1], [2], [3], [6], [8], [12] and [15] . For more reference related to the problems of the convergence of the Fourier-Laplace series on unit sphere we refer the readers to [20].…”

“…In current work we extend the latter result for the case of the Riesz means of the spectral expansions of the Laplace-Beltrami operator on unit sphere. Here we use the estimation for the Riesz means of the spectral function of the Laplace-Beltrami operator on sphere (see [2]). …”