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Quasiconformal Extension of Strongly Spirallike Functions

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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].

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, 980-8579, Japan

    Toshiyuki Sugawa

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  1. Toshiyuki Sugawa
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Correspondence to Toshiyuki Sugawa.

Additional information

The author was supported in part by the JSPS Grant-in-Aid for Scientific Research (B), 22340025.

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Sugawa, T. Quasiconformal Extension of Strongly Spirallike Functions. Comput. Methods Funct. Theory 12, 19–30 (2012). https://doi.org/10.1007/BF03321810

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  • DOI: https://doi.org/10.1007/BF03321810

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