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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Nevanlinna functions as quotients

Author(s): Evgueni Doubtsov
Journal: Proc. Amer. Math. Soc. 128 (2000), 2899-2901.
MSC (2000): Primary 32A35
Posted: February 28, 2000
MathSciNet review: 1690983
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Abstract | References | Similar articles | Additional information

Abstract:

Let $f$ be a holomorphic function in the unit ball. Then $f$ is a Nevanlinna function if and only if there exist Smirnov functions $f_+$, $f_-$ such that $f = f_+/f_-$ and $f_-$ has no zeros in the ball.


References:

1.
A.B. Aleksandrov, Function theory in the ball, in: Several Complex Variables II (eds. G.M. Khenkin and A.G. Vitushkin) Encyclopaedia Math. Sci., vol. 8, Springer-Verlag, Berlin, 1994, 107-178.MR 95e:32001

2.
E. Doubtsov, Henkin measures, Riesz products and singular sets, Ann. Inst. Fourier (Grenoble) 48 (1998), 699-728. CMP 98:17

3.
M.S. Gowda, Nonfactorization theorems in weighted Bergman and Hardy spaces on the unit ball of $\ensuremath{\mathbb{C}^n} $ $(n>1)$, Trans. Amer. Math. Soc. 277 (1983), 203-212. MR 84i:32005

4.
G.M. Henkin, H. Lewy's equation and analysis on a pseudoconvex manifold, II, Math. USSR-Sb. 102 (144) (1977), 63-94. MR 57:12907

5.
W. Rudin, Zeros of holomorphic functions in balls, Indag. Math. 38 (1976), 57-65. MR 52:14347

6.
H. Skoda, Valeurs au bord pour les solutions de l'opérateur $d^{\prime\prime},$et caractérisation des zéros des fonctions de la classe de Nevanlinna, Bull. Soc. Math. France 104 (1976), 225-299. MR 56:8913


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Additional Information:

Evgueni Doubtsov
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: dubtsov@math.msu.edu

DOI: 10.1090/S0002-9939-00-05446-0
PII: S 0002-9939(00)05446-0
Keywords: Nevanlinna class, Smirnov class
Received by editor(s): October 29, 1998
Posted: February 28, 2000
Communicated by: Steven R. Bell
Copyright of article: Copyright 2000, American Mathematical Society




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