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 .

**[1]**F. Bagemihl and W. Seidel,*Koebe arcs and Fatou points of normal functions*, Comment. Math. Helv.**36**(1961), 9–18. MR**0141786****[2]**Peter Lappan,*Non-normal sums and products of unbounded normal functions*, Michigan Math. J.**8**(1961), 187–192. MR**0131554****[3]**Peter Lappan,*Some results on a class of holomorphic functions*, Comment. Math. Univ. St. Paul.**18**(1970), 119–124. MR**0284585****[4]**G. R. MacLane,*Asymptotic values of holomorphic functions*, Rice Univ. Studies**49**(1963), no. 1, 83. MR**0148923**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1974-0374436-6

Keywords:
Normal function,
annular function,
Koebe value,
harmonic measure

Article copyright:
© Copyright 1974
American Mathematical Society