Hessenberg-Sobolev matrices and Favard type theorem Articles uri icon

publication date

  • January 2023

start page

  • 1

end page

  • 19


  • 1, 40


  • 46

International Standard Serial Number (ISSN)

  • 0126-6705

Electronic International Standard Serial Number (EISSN)

  • 2180-4206


  • 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.


  • Mathematics


  • sobolev orthogonality; orthogonal polynomials; moment problem; favard theorem; hessenberg matrices; hankel matrices