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Existence of Perfect Picard Sets

Published online by Cambridge University Press:  22 January 2016

Kikuji Matsumoto
Kikuji Matsumoto*
Affiliation:
Mathematical Institute, Nagoya University
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Let E be a totally disconnected compact set in the z-plane and let Ω be its complement with respect to the extended 2-plane. Then Ω is a domain and we can consider a single-valued meromorphic function f(z) in Ω which has a transcendental singularity at each point ζ ∊ E. Suppose that E is a null-set of the class W in the sense of Kametani [4] (= the class NB in the sense of Ahlfors and Beurling [1]).

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 213 - 222
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

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