On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials

2020/06/20 by Sergey M‎. ‎Zagorodnyuk, Sergey M. Zagorodnyuk, Zagorodnyuk, Sergey M.
Mathematics · Social Sciences · #42C05 #Classical Analysis and ODEs (math.CA) #Diverse Research Studies Overview #FOS: Mathematics #Mathematical functions and polynomials #math.CA #msc:42C05

paper · pdf · doi:10.48550/arxiv.2006.11554

28 pages

openalex publication_date 2020/06/20 · arxiv created 2020/09/09 · arxiv updated 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every system \ p_n(z) \_n=0^∞ of OPRL or OPUC, we construct Sobolev orthogonal polynomials y_n(z), with explicit integral representations involving p_n. Two concrete families of Sobolev orthogonal polynomials (depending on an arbitrary number of complex parameters) which are generalized eigenvalues of a difference operator (in n) and generalized eigenvalues of a differential operator (in n) are given. Applications of a general connection between Sobolev orthogonal polynomials and orthogonal systems of functions in the direct sum of scalar L²_μ spaces are discussed.

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