Hessenberg–Sobolev Matrices and Favard Type Theorem

Abstract We study the relation between certain non-degenerate lower Hessenberg infinite matrices $${\mathcal {G}}$$ G and existence of sequences orthogonal polynomials with respect to Sobolev inner products. In other words, we extend well-known Favard theorem for orthogonality. characterize structure matrix associated formal moments {M}}_{{\mathcal {G}}}$$ M in terms operators.