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Quasiconformal Extension of Strongly Spirallike Functions

Quasiconformal Extension of Strongly Spirallike Functions We show that a strongly λ-spirallike function of order α can be extended to a sin(πα/2)-quasiconformal automorphism of the complex plane for -π/2 < λ < π/2 and 0 < α < 1 with ¦λ¦ < πα/2. Towards the proof we provide several geometric characterizations of a strongly λ-spirallike domain of order α. We also give a concrete form of the mapping function of the standard strongly λ-spirallike domain $U_{\lambda,\alpha}$ of order α. A key tool of the present study is the notion of λ-argument, which was developed by Y. C. Kim and the author [5]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Quasiconformal Extension of Strongly Spirallike Functions

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Publisher
Springer Journals
Copyright
Copyright © 2012 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/BF03321810
Publisher site
See Article on Publisher Site

Abstract

We show that a strongly λ-spirallike function of order α can be extended to a sin(πα/2)-quasiconformal automorphism of the complex plane for -π/2 < λ < π/2 and 0 < α < 1 with ¦λ¦ < πα/2. Towards the proof we provide several geometric characterizations of a strongly λ-spirallike domain of order α. We also give a concrete form of the mapping function of the standard strongly λ-spirallike domain $U_{\lambda,\alpha}$ of order α. A key tool of the present study is the notion of λ-argument, which was developed by Y. C. Kim and the author [5].

Journal

Computational Methods and Function TheorySpringer Journals

Published: Aug 24, 2011

References