Baire category principle and uniqueness theorem
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- by J. S. Hwang PDF
- Trans. Amer. Math. Soc. 266 (1981), 655-665 Request permission
Abstract:
Applying a theorem of Bagemihl and Seidel (1953), we prove that if ${S_2}$ is a set of second category in $(\alpha ,\beta )$, where $0 \leqslant \alpha < \beta \leqslant 2\pi$, and if $f(z)$ is a function meromorphic in the sector $\Delta (\alpha ,\beta ) = \{ z:0 < \left | z \right | < \infty ,\alpha < \arg z < \beta \}$ for which ${\underline {{\operatorname {lim}}} _{r \to \infty }}\left | {f(r{e^{i\theta }})} \right | > 0$, for all $\theta \in {S_2}$, then there exists a sector $\Delta (\alpha ’,\beta ’) \subseteq \Delta (\alpha ,\beta )$ such that $(\alpha ’,\beta ’) \subseteq {\bar S_2},{S_2}$ is second category in $(\alpha ’,\beta ’)$, and $f(z)$ has no zero in $\Delta (\alpha ’,\beta ’)$. Based on this property, we prove several uniqueness theorems.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 266 (1981), 655-665
- MSC: Primary 30D40; Secondary 30D50
- DOI: https://doi.org/10.1090/S0002-9947-1981-0617558-2
- MathSciNet review: 617558