On a class of Sobolev scalar products in the polynomials

This paper discusses Sobolev orthogonal polynomials for a class of scalar products that contains the sequentially dominated products introduced by G. L. Lagomasino and H. Pijeira. We prove asymptotics for Markov type functions associated to the Sobolev scalar product and an extension of Widom’s Theorem on the location of the zeroes of the orthogonal polynomials. In the case of measures supported in the real line, we obtain results related to the determinacy of the Sobolev moment problem and the completeness of the polynomials in a suitably defined weighted Sobolev space.