Hessenberg-Sobolev matrices and Favard type theorem

We study the relation between certain non-degenerate lower Hessenberg infinite matrices G and the existence of sequences of orthogonal polynomials with respect to Sobolev inner products. In other words, we extend the well-known Favard theorem for Sobolev orthogonality. We characterize the structure of the matrix G and the associated matrix of formal moments MG in terms of certain matrix operators.The research of I. Pérez-Yzquierdo was partially supported by Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico (FONDOCYT), Dominican Republic, under grant 2016-2017-080 No. 013-2018. The authors thank the reviewers for theirs constructive comments and suggestions that helped to improve the clarity of this manuscript. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature