Asymptotic zero distribution for a class of multiple orthogonal polynomials
Asymptotic zero distribution for a class of multiple orthogonal polynomials
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DOI：
10.1090/s0002-9947-08-04535-2
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发表时间：
2006-06
影响因子：
1.3
通讯作者：
Els Coussement;J. Coussement;W. Assche
中科院分区：
文献类型：
--
作者：
Els Coussement;J. Coussement;W. Assche
本文建立了具有特定极限性质的四项变递归系数递归关系所生成的多项式的渐近零分布。证明是基于这些多项式的比率渐近性。我们可以将这个结果应用到三个多重正交多项式的例子中，特别是Jacobi-Pineiro， Laguerre I和与修正贝塞尔函数相关的例子。我们还讨论了Toeplitz矩阵的一个应用。
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-Pineiro, Laguerre I and the example associated with modified Bessel functions. We also discuss an application to Toeplitz matrices.