Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions

In this paper we consider the polynomials {Pnμ,ν(x)}n=0∞, orthogonal with respect to a certain symmetric bilinear form of Sobolev type. These polynomials are the result of two linear perturbations to the orthogonal polynomials {Pn(x)}n=0∞, eigenfunctions of a linear differential or difference operator L. We show that the polynomials {Pnμ,ν(x)}n=0∞ are eigenfunctions of one or more linear differential or difference operators (possibly of infinite order) of the form L + μA + νB + μνC.