General Sobolev Orthogonal Polynomials

AbstractIn this paper, we study orthogonal polynomials with respect to the inner product (f,g)S(N) =〈u,fg〉+∑m=1N λm〈u,f(m)g(m) 〉, where λm≥0 form=1,…,N, anduis 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 withu