Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems

被引：7

作者：

Erb, Wolfgang ^{[2
]}

Tookos, Ferenc ^{[1
]}

机构：

[1] Helmholtz Ctr Munich, Inst Biomath & Biometry, D-85764 Neuherberg, Germany

[2] Univ Lubeck, Inst Math, D-23560 Lubeck, Germany

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 09期

关键词：

Monotonicity of zeros; Associated Jacobi polynomials; Associated Gegenbauer polynomials; q-Meixner-Pollaczek polynomials; Interlacing of zeros; Orthogonal polynomials on the unit ball; JACOBI-POLYNOMIALS; ULTRASPHERICAL POLYNOMIALS; INEQUALITIES;

D O I：

10.1016/j.amc.2010.11.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate monotonicity properties of extremal zeros of orthogonal polynomials depending on a parameter. Using a functional analysis method we prove the monotonicity of extreme zeros of associated Jacobi, associated Gegenbauer and q-Meixner-Pollaczek polynomials. We show how these results can be applied to prove interlacing of zeros of orthogonal polynomials with shifted parameters and to determine optimally localized polynomials on the unit ball. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：4771 / 4780

页数：10

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