Geometric properties of inverse polynomial images

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Abstract

Given a polynomial Tn of degree n, consider the inverse image of R and [-1, 1], denoted by Tn-1(R) and Tn-1([-1, 1]), respectively. It is well known that Tn-1(R) consists of n analytic Jordan arcs moving from ∞ to ∞. In this paper, we give a necessary and sufficient condition such that (1) Tn-1([-1, 1]) consists of ν analytic Jordan arcs and (2) Tn-1([-1, 1]) is connected, respectively.

Original languageEnglish
Title of host publicationApproximation Theory XIII
Subtitle of host publicationSan Antonio 2010
Pages277-287
Number of pages11
DOIs
Publication statusPublished - 2012
Event13th International Conference on Approximation Theory, ICAT 2010 - San Antonio, TX, United States
Duration: 7 Mar 201010 Mar 2010

Publication series

NameSpringer Proceedings in Mathematics
Volume13
ISSN (Print)2190-5614
ISSN (Electronic)2190-5622

Conference

Conference13th International Conference on Approximation Theory, ICAT 2010
Country/TerritoryUnited States
CitySan Antonio, TX
Period07.03.201010.03.2010

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