Lebesgue Sobolev orthogonality on the unit circle
type: Item
instance of: scholarly article
title: Lebesgue Sobolev orthogonality on the unit circle
zbMATH Open document ID: 0933.42011
DOI: 10.1016/S0377-0427(98)00089-2
published in: Journal of Computational and Applied Mathematics
publication date: 2000-03-12T00:00:00Z
review text: This is a very nicely written paper extending results for monic orthogonal polynomials \(P_n\) as \(n\rightarrow\infty\) on growth of the norm, pointwise limits and the radius of the disk containing all zeros to the case of the following Sobolev inner product on the unit circle: \[ \langle f(z),g(z)\rangle_s=\int_0^{2\pi} f(e^{i\theta})\overline{g(e^{i\theta})} d\mu(\theta) + \sum_{k=1}^p \lambda_k \int_0^{2\pi} f^{(k)}(e^{i\theta})\overline{g^{(k)}(e^{i\theta})} {d\theta\over 2\pi},\quad z=e^{i\theta}, \] where \(d\mu(\theta)\) is a finite positive Borel measure on \([0,2\pi]\) with infinite support, verifying the Szegő condition and with \(\lambda_1>0\), \(\lambda_k\geq 0\;(2\leq k\leq p), d\theta/2\pi\) the normalized Lebesgue measure on \([0,2\pi]\).
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1326429
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Sobolev inner products
zbMATH Keywords: measures on the unit circle
zbMATH Keywords: Szegő condition
author: E. Berriochoa
author: A. Cachafeiro
reviewed by: Marcel G. de Bruin
MaRDI profile type: Publication
cites work: A Convergence Equivalence Related to Polynomials Orthogonal on the Unit Circle
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cites work: A class of orthogonal polynomials
cites work: Q3270024
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cites work: On polynomials orthogonal with respect to certain Sobolev inner products
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description: scientific article; zbMATH DE number 1326429