Exceptional values of analytic functions
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- by P. Krajkiewicz PDF
- Proc. Amer. Math. Soc. 40 (1973), 159-165 Request permission
Abstract:
Let $g(z)$ be an analytic function with an isolated singularity at ${z_0}$ and let $f(z)$ be a nonanalytic multianalytic function with a nonessential isolated singularity at ${z_0}$. It is shown that if $g(z) - f(z)$ does not vanish in some deleted neighborhood of ${z_0}$, then ${z_0}$ is a nonessential singularity of $g(z)$.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
- P. Krajkiewicz, Bianalytic functions with exceptional values, Proc. Amer. Math. Soc. 38 (1973), 75–79. MR 313519, DOI 10.1090/S0002-9939-1973-0313519-2 P. Montel, Leçons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, 1927.
- P. C. Rosenbloom, The fix-points of entire functions, Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (1952), no. Tome Supplémentaire, 186–192. MR 51916
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 159-165
- MSC: Primary 30A72
- DOI: https://doi.org/10.1090/S0002-9939-1973-0330466-0
- MathSciNet review: 0330466