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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
    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
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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