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Cluster Points and Asymptotic Values of C 1- and Planar Harmonic Functions

Cluster Points and Asymptotic Values of C 1- and Planar Harmonic Functions A sufficient condition for a cluster point of a C 1-functio on ℝ2 to be an asymptotic value is given, based on a partitioning into regions of constant valence. We also obtain a sufficient condition for the cluster set of a planar harmonic function to have non-empty interior. An example is given of a planar harmonic function where the image of the critical set is not closed and such that the cluster set has non-empty interior and is a proper subset of the image. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Cluster Points and Asymptotic Values of C 1- and Planar Harmonic Functions

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Publisher
Springer Journals
Copyright
Copyright © 2007 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321643
Publisher site
See Article on Publisher Site

Abstract

A sufficient condition for a cluster point of a C 1-functio on ℝ2 to be an asymptotic value is given, based on a partitioning into regions of constant valence. We also obtain a sufficient condition for the cluster set of a planar harmonic function to have non-empty interior. An example is given of a planar harmonic function where the image of the critical set is not closed and such that the cluster set has non-empty interior and is a proper subset of the image.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 19, 2007

References