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arXiv · 2006.11554

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

Sergey M. Zagorodnyuk
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Abstract

For every system $\{ p_n(z) \}_{n=0}^\infty$ 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 $L^2_\mu$ spaces are discussed.

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Sergey M. Zagorodnyuk. 2020-06-20. On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials. https://arxiv.org/abs/2006.11554

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