Product Formulas and Associated Hypergroups for Orthogonal Polynomials on the Simplex and on a Parabolic Biangle

Abstract

Explicit product formulas are obtained for families of multivariate polynomials which are orthogonal on simplices and on a parabolic biangle in ${\Bbb R}^2$ . These product formulas are shown to give rise to measure algebras which are hypergroups. The article also includes an elementary proof that the Michael topology for the space of compact subsets of a topological space (which is used in the definition of a hypergroup) is equivalent to the Hausdorff metric topology when the underlying space has a metric.