General Sobolev Orthogonal Polynomials

In this paper, we study orthogonal polynomials with respect to the inner product f,g.S N.s u, fg:q mNs1lm u,f m.g m.:, where lmG0 for ms1, . . . , N, and u is a semiclassical, positive definite linear functional. For these non-standard orthogonal polynomials, algebraic and differential properties are obtained, as well as their representation in terms of the standard orthogonal polynomials associated with u.