Strong unboundedness of unbounded analytic functions
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- by A. Ya. Gordon PDF
- Proc. Amer. Math. Soc. 122 (1994), 525-529 Request permission
Abstract:
It is proved that if f is an unbounded analytic function in the open unit disc $\mathbb {D}$, then there must exist a sequence $({z_n})$ in $\mathbb {D}$ such that for every $j = 0,1,2, \ldots ,{f^{(j)}}({z_n}) \to \infty$ as $n \to \infty$. This answers affirmatively a question asked by J. Langley and L. Rubel in 1984.References
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J. Langley and L. A. Rubel, Some problems about unbounded analytic functions, 199 Research Problems, Lecture Notes in Math., vol. 1043, Springer, New York, 1984, pp. 595-596.
- Lee A. Rubel, Unbounded analytic functions and their derivatives on plane domains, Bull. Inst. Math. Acad. Sinica 12 (1984), no. 4, 363–377. MR 794407
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 525-529
- MSC: Primary 30D30
- DOI: https://doi.org/10.1090/S0002-9939-1994-1204374-0
- MathSciNet review: 1204374