Inverse images of polynomial mappings and polynomials orthogonal on them.
type: Item
instance of: scholarly article
title: Inverse images of polynomial mappings and polynomials orthogonal on them.
zbMATH Open document ID: 1034.30002
DOI: 10.1016/S0377-0427(02)00628-3
author: Franz Peherstorfer
published in: Journal of Computational and Applied Mathematics
publication date: 2003-05-22T00:00:00Z
review text: Let \(T\) be a polynomial with complex coefficients. First, the author studies the inverse images of the real and imaginary axes under \(T\) in detail. Then for an arbitrary polynomial \(\rho\) and a sequence \((p_n)_{n\in \mathbb{N}}\) of orthogonal polynomials the orthogonality behaviour of the sequence of polynomials \((\rho (p_n \circ T))_{n\in \mathbb{N}}\) is investigated. In particular, necessary and sufficient conditions are given such that \((\rho (p_n \circ T))_{n\in \mathbb{N}}\) is a subsequence of polynomials orthogonal with respect to a positive measure supported on a compact subset of the real line.
reviewed by: W. Koepf
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1915250
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: polynomial mappings
zbMATH Keywords: inverse images
zbMATH Keywords: functionals
zbMATH Keywords: positive measure
zbMATH Keywords: positive definite
MaRDI profile type: Publication
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full work available at URL: s0377-0427(02)00628-3
OpenAlex ID: W2045877951
description: scientific article; zbMATH DE number 1915250