The growth of Laguerre matrix polynomials on bounded intervals

被引：19
|
作者：
Jódar, L
Sastre, J
机构：
[1] Univ Politecn Valencia, Dept Matemat Aplicada, Valencia, Spain
[2] Univ Politecn Valencia, Dept Comunicac, E-46071 Valencia, Spain
来源：
APPLIED MATHEMATICS LETTERS | 2000年 / 13卷 / 08期
关键词：
Laguerre matrix polynomials; gamma function; asymptotics;
D O I：
10.1016/S0893-9659(00)00090-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let A be a matrix in C-rxr such that Re(z) > -1/2 for all the eigenvalues of A and let {IIn(A,1/2) (x)} be the normalized sequence of Laguerre matrix polynomials associated with A. this paper, it is proved that IIn(A,1/2) (x) = O(n(alpha>(*) over bar * (A)/2)ln(r-1)(n)) and IIn+1(A,1/2) (x) = O(n((alpha>(*) over bar * (A)-1)/2)In(r-1)(n)) uniformly on bounded intervals, where alpha>(*) over bar * (A) = max{Re(z); z eigenvalue of A}. (C) 2000 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：21 / 26
页数：6
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