A density result concerning inverse polynomial images

In this paper, we consider polynomials of degree n for which the inverse image of [−1, 1] consists of two Jordan arcs. We prove that the four endpoints of these arcs form an O(1/n)-net in the complex plane.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2014-02, Vol.142 (2), p.539-545
Main Author: SCHIEFERMAYR, KLAUS
Format: Article
Language:English
Subjects:
Approximation
Degrees of polynomials
Elliptic functions
Geometric planes
Hypergeometric functions
Jacobians
Mathematical intervals
Mathematical theorems
Polynomials
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Description
Summary:In this paper, we consider polynomials of degree n for which the inverse image of [−1, 1] consists of two Jordan arcs. We prove that the four endpoints of these arcs form an O(1/n)-net in the complex plane.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2013-11770-3