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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of $ F\sp{+}\cap N$


Author: M. Stoll
Journal: Proc. Amer. Math. Soc. 57 (1976), 97-98
DOI: https://doi.org/10.1090/S0002-9939-1976-0399471-5
MathSciNet review: 0399471
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Abstract: In this note we give a characterization of $ {F^ + } \cap N$, where $ N$ denotes the Nevanlinna class of functions of bounded characteristic and $ {F^ + }$ denotes the containing Fréchet space of $ {N^ + }$. We show that a holomorphic function $ f \in {F^ + } \cap N$ if and only if $ f(z) = g(z)/{S_\mu }(z)$, where $ g \in {N^ + }$ and $ {S_\mu }$ is a singular inner function with respect to a nonnegative continuous singular measure $ \mu $.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0399471-5
Article copyright: © Copyright 1976 American Mathematical Society