Hessenberg –Sobolev Matrices and Favard Type Theorem
Hessenberg –Sobolev Matrices and Favard Type Theorem
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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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Pérez Yzquierdo, I. (2022). Hessenberg–Sobolev Matrices and Favard Type Theorem. Bulletin of the Malaysian Mathematical Sciences Society, 46(1), 40.