Laguerre-type operators, Special functions and Applications

The monomiality principle was introduced (see e.g. [1] and the references therein) in order to derive properties of special polynomials from the corresponding ones holding for monomials. A set of paramount importance in this framework is given by the Hermite-Kampé de Fériet (shortly H-KdF) or Gould-Hopper polynomials [2], [3], [4]. As it is well known, the Hermite-Kampé de Fériet polynomials H n (x, y) are called heat polynomials [5], since they are elementary solutions of the heat equation in the half-plane, but they enter even in the explicit solutions of many classical or pseudo-classical BVP (see [6], [7]). The relevant results were generalized to many variables problems in [8], [9]. The so called two variable Laguerre polynomials are defined by: