Inverse images of polynomial mappings and polynomials orthogonal on them

被引：15

作者：

Peherstorfer, F ^{[1
]}

机构：

[1] Johannes Kepler Univ, Inst Anal & Numer, A-4040 Linz, Austria

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2003年 / 153卷 / 1-2期

关键词：

orthogonal polynomials; polynomial mappings; inverse images; functionals; positive measure; positive definite;

D O I：

10.1016/S0377-0427(02)00628-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let T be a polynomial with complex coefficients. First, we study the inverse images of the real and imaginary axes under a polynomial mapping T in detail. Then for an arbitrary polynomial rho and a sequence (p(n)) of orthogonal polynomials the orthogonality behaviour of the sequence of polynomials (rho(p(n) o T))(nis an element ofN) is investigated. In particular necessary and sufficient conditions are given such that (rho(p(n) o T))(nis an element ofN) is a subsequence of polynomials orthogonal with respect to a positive measure supported on a compact subset of the real line. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：371 / 385

页数：15

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