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Description of Inverse Polynomial Images which Consist of Two Jordan Arcs with the Help of Jacobi’s Elliptic Functions

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Abstract

First we discuss the description of inverse polynomial images of [−1,1], which consists of two Jordan arcs, by the endpoints of the arcs only. The polynomial which generates the two Jordan arcs is given explicitly in terms of Jacobi’s theta functions. Then we concentrate on the case where the two arcs are symmetric with respect to the real line. In particular it is shown that the endpoints vary monotonically with respect to the modulus k of the associated elliptic functions.

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Authors and Affiliations

  1. Institut für Analysis, Abteilung für dynamische Systeme und Approximationstheorie, Universität Linz, Altenbergerstraβe 69, A-4040, Linz, Austria

    Franz Peherstorfer

  2. Department for Automation Engineering, University of Applied Sciences, Roseggerstr. 12, A-4600, Wels, Austria

    Klaus Schiefermayr

Authors
  1. Franz Peherstorfer
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  2. Klaus Schiefermayr
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Correspondence to Franz Peherstorfer.

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This work was supported by the Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” (FWF), project numbers P10737-TEC and P16390-N04.

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Peherstorfer, F., Schiefermayr, K. Description of Inverse Polynomial Images which Consist of Two Jordan Arcs with the Help of Jacobi’s Elliptic Functions. Comput. Methods Funct. Theory 4, 355–390 (2005). https://doi.org/10.1007/BF03321075

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