Bianalytic functions with exceptional values
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- by P. Krajkiewicz
- Proc. Amer. Math. Soc. 38 (1973), 75-79
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313519-2
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Abstract:
Let $f(z,\bar z)$ be a bianalytic function which omits the value zero in some deleted neighborhood $A$ of an isolated singularity ${z_0}$. It is shown that there is a function $g(z)$ analytic on $A$ and a function $h(z,\bar z)$ bianalytic on $A$ with a nonessential singularity at ${z_0}$ such that $f(z,\bar z) = g(z)h(z,\bar z)$ on $A$.References
- M. B. Balk, Entire poly-analytic functions with a bounded set of zeros, Izv. Akad. Nauk Armjan. SSR Ser. Mat. 1 (1966), no. 5, 341–357 (Russian, with Armenian and English summaries). MR 0206308
- W. Bosch and P. Krajkiewicz, The big Picard theorem for polyanalytic functions, Proc. Amer. Math. Soc. 26 (1970), 145–150. MR 264096, DOI 10.1090/S0002-9939-1970-0264096-3 H. Cartan, Sur les zéroes des combinaisons linéaires de $p$ fonctions holomorphes données, Mathematica (Cluj) 7 (1933), 5-31. P. Montel, Leçons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, 1927.
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 75-79
- MSC: Primary 30A92
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313519-2
- MathSciNet review: 0313519