Recursive Procedures for Krall-Sheffer Operators

Abstract

We consider the Krall-Sheffer class of admissible, partial differential operators in the plane. We concentrate on algebraic structures, such as the role of commuting operators and symmetries. For the polynomial eigenfunctions, we give explicit forms of the the $3-$level recurrence relations and differential raising operators, which are shown to satisfy unusual commutation relations. We present new generating functions for two of the cases.