The present paper deals with the solution of an inverse problem
in the theory of orthogonal polynomials. It was motivated by a
characterization result concerning sequences of polynomials orthogonal
with respect to a Sobolev inner product when they can be recursively
generated in terms of orthogonal polynomial sequences associated
with the measure involved in the standard component. More precisely,
we obtain the set of pairs of quasi-definite linear functionals such
that their corresponding sequences of monic orthogonal polynomials
{Pn} and {Rn} are related by a
differential expression.