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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An annular function which is the sum of two normal functions


Author: Peter Lappan
Journal: Proc. Amer. Math. Soc. 44 (1974), 403-408
MSC: Primary 30A72
MathSciNet review: 0374436
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Abstract: It is known that a nonconstant normal function cannot have a Koebe value. An example is presented of an annular function which is the sum of two normal holomorphic functions. This example shows that a sum of two normal functions can result in a nonconstant function which has the Koebe value $ \infty $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0374436-6
PII: S 0002-9939(1974)0374436-6
Keywords: Normal function, annular function, Koebe value, harmonic measure
Article copyright: © Copyright 1974 American Mathematical Society