Hessenberg – Sobolev matrices and Favard type theorem
Hessenberg – Sobolev matrices and Favard type theorem
Date
2022-12-01
Authors
Ignacio Pérez Yzquierdo
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Abstract
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.
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Citation
Pijeira-Cabrera, H., Decalo-Salgado, L. & Pérez-Yzquierdo, I. Hessenberg–Sobolev Matrices and Favard Type Theorem. Bull. Malays. Math. Sci. Soc. 46, 40 (2023).