Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
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$.


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

  • [1] M. B. Balk, On the values taken by entire polyanalytic functions, Dokl. Akad. Nauk SSSR 167 (1966), 12–15 (Russian). MR 0199398
  • [2] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038
  • [3] P. Montel, Leçons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, 1927.
  • [4] Walter Saxer, Über eine Verallgemeinerung des Satzes von Schottky, Compositio Math. 1 (1935), 207–216 (German). MR 1556887

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30.61

Retrieve articles in all journals with MSC: 30.61


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0264096-3
Keywords: Picard's big theorem, polyanalytic functions, essential isolated singularity, Poisson-Jensen integral formula, quasi-normal families
Article copyright: © Copyright 1970 American Mathematical Society