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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strong unboundedness of unbounded analytic functions


Author: A. Ya. Gordon
Journal: Proc. Amer. Math. Soc. 122 (1994), 525-529
MSC: Primary 30D30
MathSciNet review: 1204374
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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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] 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 (86f:30029)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1204374-0
PII: S 0002-9939(1994)1204374-0
Article copyright: © Copyright 1994 American Mathematical Society