Jackson's (-1)-Bessel functions with the Askey-Wilson algebra setting
Chorfi,, Bouzeffour, F Jedidi, W . 2015
Abstract
This work is devoted to the study of some functions arising from a limit transition of the Jackson q-Bessel functions when q tends to -1. These functions coincide with the so-called cas function for particular values of parameters. We prove that there are eigenfunctions of differential-difference operators of Dunkl-type. Also we consider special cases of the Askey-Wilson algebra , which have these operators (up to constants) as one of their three generators and whose defining relations are given in terms of anti-commutators.
Abstract
The aim of this paper is to prove Heisenberg-Pauli-Weyl inequality for a fractional power of the Dunkl transform on the real line for which there is an index law and a Plancherel…
Abstract
In this paper we consider the differential-difference reflection operator associated with a finite cyclic group,
Y(v)f(x) = df(x)/dx + Sigma(m-1)(i-1)mv(i) + m - i/x Sigma(…