A Generalization of Favard′s Theorem for Polynomials Satisfying a Recurrence Relation Original Research Article

In this paper, we give the canonical expression for an inner product (delined in P the linear space of real polynomials), for which the set of orthonormal polynomials satisfies a (2N + 1)-term recurrence relation. This result is a generalization of Favard′s theorem about orthogonal polynomials and three-term recurrence relations. Also, we characterize these inner products in terms of symmetric operators. Similar results are proved for some kinds of discrete Sobolev inner products.