On discrete orthogonal polynomials of several variables

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, [email protected]?"x"@?"Vf(x)@r(x), where @r is a nonzero function on V. Polynomial subspaces that contain discrete orthogonal polynomials with respect to the bilinear form =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.