ON ORTHOGONAL POLYNOMIALS WITH RESPECT TO CERTAIN DISCRETE SOBOLEV INNER PRODUCT

被引：10

作者：

Marcellan, Francisco ^{[1
]}

Zejnullahu, Ramadan

Fejzullahu, Bujar

Huertas, Edmundo ^{[1
]}

机构：

[1] Univ Carlos III Madrid, Escuela Politecn Super, Dept Matemat, Leganes 28911, Spain

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2012年 / 257卷 / 01期

关键词：

orthogonal polynomials; discrete Sobolev polynomials; Laguerre polynomials; asymptotics; RELATIVE ASYMPTOTICS; LAGUERRE-POLYNOMIALS; SPACE; ZEROS;

D O I：

10.2140/pjm.2012.257.167

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we deal with sequences of polynomials orthogonal with respect to the discrete Sobolev inner product < f, g > s = f(0)(infinity) omega(x) f (x)g(x)dx + Mf(xi)g(xi) + Nf'(xi)g'(xi), where omega is a weight function, xi <= 0, and M, N >= 0. The location of the zeros of discrete Sobolev orthogonal polynomials is given in terms of the zeros of standard polynomials orthogonal with respect to the weight function omega. In particular, for omega(x) = x(alpha)e(-x) we obtain the asymptotics for discrete Laguerre-Sobolev orthogonal polynomials.

引用

页码：167 / 188

页数：22

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