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Lebesgue Sobolev orthogonality on the unit circle

✍ Scribed by E. Berriochoa; A. Cachafeiro

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
294 KB
Volume
96
Category
Article
ISSN
0377-0427

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✦ Synopsis

This paper is devoted to the study of asymptotic properties of the orthogonal polynomials with respect to a Sobolev inner product 2n P /'2n ('(z),y(z))s= fo '(eiO)~d/~(0)+ ~2' J0 f(k'(eiO)~2~' z= eiΒ°' with d/~(0) a finite positive Borel measure on [0,2n] with an infinite set as support verifying the Szeg6 condition, 21 > 0, 2k ~> 0 (k = 2 ..... p) and dO/2n the normalized Lebesgue measure on [0, 21t].

Our aim is to extend some previous results that we have obtained in [2,3] when the measure /~ belongs to the Bemstein-Szeg6 class and p = 1. (~) 1998 Elsevier Science B.V. All fights reserved.

πŸ“œ SIMILAR VOLUMES

A family of Sobolev orthogonal polynomia
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We study the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product on the unit circle is a M\_M positive definite matrix or a positive semidefinite diagonal block matrix, M=l 1 + } } } +l m +m, d+ belongs to a certain class of measures, and