Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Polyanalytic functions with exceptional values

Author: P. Krajkiewicz
Journal: Trans. Amer. Math. Soc. 197 (1974), 181-210
MSC: Primary 30A92; Secondary 30A70
MathSciNet review: 0350024
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Abstract: Let $ f(z) = \sum\nolimits_{k = 0}^n {{{\bar z}^k}{f_k}(z)} $ where the functions $ {f_0},{f_1}, \cdots ,{f_n}$ are analytic on some annular neighborhood A of the point $ \infty $ and $ {f_n} \equiv 1$ on A and z denotes the complex conjugate of z. If f does not vanish on A it is shown that the functions $ {f_0},{f_1}, \cdots ,{f_{n - 1}}$ have a nonessential isolated singularity at the point infinity.

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Keywords: Polyanalytic functions, polyentire functions, essential isolated singularity, exceptional values, Picard's big theorem
Article copyright: © Copyright 1974 American Mathematical Society