Hessenberg-Sobolev Matrices and Favard type theorems

2022/06/11 by Pijeira-Cabrera, Hector, Decalo-Salgado, Laura, Perez-Yzquierdo, Ignacio
#11B37 #30E05 #33C47 #42C05 #44A60 #47B35 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.05612

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 M_G in terms of certain matrix operators.

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