Multiplicity of zeros and discrete orthogonal polynomials

被引：0

作者：

Krasikov I. ^{[1
]}

机构：

[1] Department of Mathematical Sciences, Brunei University, Uxbridge

来源：

Results in Mathematics | 2004年 / 45卷 / 1-2期

关键词：

Classical Orthogonal Polynomial; Distance Distribution; Laguerre Polynomial; Orthogonal Polynomial; Prescribe Norm;

D O I：

10.1007/BF03322997

中图分类号：

学科分类号：

摘要：

We consider a problem of bounding the maximal possible multiplicity of a zero of some expansions Σ aiFi(x), at a certain point c, depending on the chosen family {imi}. The most important example is a polynomial with c = 1. It is shown that this question naturally leads to discrete orthogonal polynomials. Using this connection we derive some new bounds, in particular on the multiplicity of the zero at one of a polynomial with a prescribed norm. 30C15, 33C47 © 2004, Birkhäuser Verlag, Basel.

引用

页码：59 / 66

页数：7

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