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arXiv · 2206.05612

Hessenberg-Sobolev Matrices and Favard type theorems

Hector Pijeira-Cabrera·Laura Decalo-Salgado·Ignacio Perez-Yzquierdo
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Abstract

We study the relation between certain non-degenerate lower Hessenberg infinite matrices $\mathcal{G}$ 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 $\mathcal{G}$ and the associated matrix of formal moments $\mathcal{M}_{\mathcal{G}}$ in terms of certain matrix operators.

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Hector Pijeira-Cabrera, Laura Decalo-Salgado, Ignacio Perez-Yzquierdo. 2022-06-11. Hessenberg-Sobolev Matrices and Favard type theorems. https://arxiv.org/abs/2206.05612

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