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A family of Sobolev orthogonal polynomials on the unit circle

โœ Scribed by E. Berriochoa; A. Cachafeiro

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
108 KB
Volume
105
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

The aim of this paper is to study the polynomials orthogonal with respect to the following Sobolev inner product:

where is the normalized Lebesgue measure and is a rational modiรฟcation of . In this situation we analyse the algebraic results and the asymptotic behaviour of such orthogonal polynomials. Moreover some properties about the distribution of their zeros are given.

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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= eiยฐ' with d/~(0) a finite positive Borel measure on [0,2n] with an infinite set as support verifying the