Special functions associated with complex reflection groups
Bouzeffour, Fethi . 2014
In this paper, we first review the theory of Dunkl operators for complex reflection groups and then the theory of hyper-Bessel functions, which are a particular case of Meijer’s G-function and satisfy a higher order differential equation. Then we show that there exists a close relation between both theories. In fact, the components of the eigenfunctions of a Dunkl operator for a complex reflection group in the rank one case can be expressed in terms of hyper-Bessel functions.
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(…