Computational Methods and Function Theory 4 (2004), No. 2, 355--390
Copyright Heldermann Verlag 2004
Franz Peherstorfer
franz.peherstorfer@jku.at , Johannes Kepler Universität Linz, Institut für Analysis, Abteilung für dynamische Systeme und Approximationstheorie, Altenbergerstraße 69, A-4040 Linz, Austria.
Klaus Schiefermayr
k.schiefermayr@fh-wels.at , University of Applied Sciences, Department for Automation Engineering, Roseggerstr. 12, A-4600 Wels, Austria.
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.
Keywords: Polynomials, ellipitc functions, theta functions, inverse
MSC 2000: 30C10, 33E05, 30E10, 41A10.
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