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Neo-Normal Functions in Arbitrary Regions

Published online by Cambridge University Press:  22 January 2016

Kam-Fook Tse
Kam-Fook Tse*
Affiliation:
Syracuse University
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It is well known that many properties possessed by functions holomorphic and bounded in a region are also possessed by functions meromorphic and omitting three values. Noshiro [14] in 1938 and Lehto and Virtanen [12] in 1957 independently defined the notion of “normal functions” ; they and many others subsequently discovered that most properties concerning boundary behavior and value distribution acquired by meromorphic functions omitting three values in the unit disk (or more general, in a simply-connected region) are also valid properties of “normal functions” defined there. In their research on the problems of value distribution of normal functions, Lange [9], Gavrilov [5] and Gauthier [4] have discovered that functions normal in the disk are exactly those which omit three values “locally,” i.e., they do not possess any “p-sequence” (see above references). However, the definition of a function being normal in a region depends on the simply-connectedness of the region or its universal covering surface. It is thus difficult to judge if a function defined in an arbitrary region is normal.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 48 , December 1972 , pp. 19 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

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