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

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 ar...

Full description

Saved in:
Bibliographic Details
Published in:Computational methods and function theory 2005-05, Vol.4 (2), p.355-390
Main Authors: Peherstorfer, Franz, Schiefermayr, Klaus
Format: Article
Language:English
Subjects:
Elliptic functions
Mathematical analysis
Polynomials
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1617-9447
2195-3724
DOI:10.1007/BF03321075