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Proceedings of the American Mathematical Society

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



The big Picard theorem for polyanalytic functions

Authors: W. Bosch and P. Krajkiewicz
Journal: Proc. Amer. Math. Soc. 26 (1970), 145-150
MSC: Primary 30.61
MathSciNet review: 0264096
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Abstract: Let $ f,g$, and $ h$ be polyanalytic in an annular neighborhood $ A$ of a complex number $ {z_0}$, finite or infinite, such that $ g$ and $ h$ do not have an essential singularity at $ {z_0}$ and $ g-h$ is not identically zero on $ A$. It is shown that if $ f-g$ and $ f-h$ never vanish on $ A$, then $ {z_0}$ is not an essential singularity of $ f$.

References [Enhancements On Off] (What's this?)

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Keywords: Picard's big theorem, polyanalytic functions, essential isolated singularity, Poisson-Jensen integral formula, quasi-normal families
Article copyright: © Copyright 1970 American Mathematical Society