On discrete orthogonal polynomials of several variables

Abstract

Let V be a set of isolated points in R d . Define a linear functional L on the space of real polynomials restricted on V, Lf=∑ x∈Vf(x)ρ(x) , where ρ is a nonzero function on V. Polynomial subspaces that contain discrete orthogonal polynomials with respect to the bilinear form 〈f,g〉= L(fg) are identified. One result shows that the discrete orthogonal polynomials still satisfy a three-term relation and Favard's theorem holds in this general setting.