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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:
Let be a holomorphic function in the unit ball. Then is a Nevanlinna function if and only if there exist Smirnov functions , such that and 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
, 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
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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