General Sobolev orthogonal polynomials

In this paper, we study orthogonal polynomials with respect to the inner product (f, g)(S)((N)) = [u, fg] + Sigma(m=1)(N) lambda(m)[u, f((m))g((m))], where lambda(m) greater than or equal to 0 for m = 1,..., 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. (C) 1996 Academic Press, Inc.