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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0264096-3
MathSciNet review:
0264096
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 $f$.
- M. B. Balk, On the values taken by entire polyanalytic functions, Dokl. Akad. Nauk SSSR 167 (1966), 12–15 (Russian). MR 0199398
- W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038 P. Montel, Leçons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, 1927.
- Walter Saxer, Über eine Verallgemeinerung des Satzes von Schottky, Compositio Math. 1 (1935), 207–216 (German). MR 1556887
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30.61
Retrieve articles in all journals with MSC: 30.61
Additional Information
Keywords:
Picard’s big theorem,
polyanalytic functions,
essential isolated singularity,
Poisson-Jensen integral formula,
quasi-normal families
Article copyright:
© Copyright 1970
American Mathematical Society