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A density result concerning inverse polynomial images


Author: Klaus Schiefermayr
Journal: Proc. Amer. Math. Soc. 142 (2014), 539-545
MSC (2010): Primary 30C10, 30E10, 33E05, 41A50
DOI: https://doi.org/10.1090/S0002-9939-2013-11770-3
Published electronically: October 22, 2013
MathSciNet review: 3133995
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Abstract: 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 $ {\mathcal O}(1/n)$-net in the complex plane.


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Additional Information

Klaus Schiefermayr
Affiliation: School of Engineering and Environmental Sciences, University of Applied Sciences Upper Austria, Stelzhamerstr.23, 4600 Wels, Austria
Email: klaus.schiefermayr@fh-wels.at

DOI: https://doi.org/10.1090/S0002-9939-2013-11770-3
Keywords: Density result, inverse polynomial image, Jacobian elliptic function, Jordan arc
Received by editor(s): October 24, 2011
Received by editor(s) in revised form: February 24, 2012, and March 19, 2012
Published electronically: October 22, 2013
Communicated by: Walter Van Assche
Article copyright: © Copyright 2013 American Mathematical Society

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