Orthogonal and pseudo-orthogonal multi-dimensional Appell polynomials

摘要

More than one hundred years ago, Appell introduced a polynomials class characterized by the exponential form of its generator function. This class is well-known on R and the aim of this paper is to offer a multi-dimensional analysis in two directions: we indicate a classical characterization of the Appell polynomials on Rd via their generator function and we investigate their orthogonality. Two types of orthogonality are characterized. We relate this study to the theory of Lie algebras and martingales.