Asymptotic zero distribution for a class of multiple orthogonal polynomials

被引：29

作者：

Coussement, E. ^{[1
]}

Coussement, J. ^{[1
]}

Van Assche, W. ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, B-3001 Louvain, Belgium

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 360卷 / 10期

关键词：

multiple orthogonal polynomials; asymptotics;

D O I：

10.1090/S0002-9947-08-04535-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these polynomials. We can apply this result to three examples of multiple orthogonal polynomials, in particular Jacobi-Pinneiro, Laguerre I and the example associated with modified Bessel functions. We also discuss an application to Toeplitz matrices.

引用

页码：5571 / 5588

页数：18

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