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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Koebe sequences of arcs and normal meromorphic functions
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by Stephen Dragosh PDF
Trans. Amer. Math. Soc. 190 (1974), 207-222 Request permission

Abstract:

Let f be a normal meromorphic function in the unit disk. An estimate for the growth of the modulus of f on a Koebe sequence of arcs is obtained; the estimate is in terms of the order of normality of f. An immediate consequence of the estimate is the following theorem due to F. Bagemihl and W. Seidel: A nonconstant normal meromorphic function has no Koebe values. Another consequence is that each level set of a nonconstant normal meromorphic function cannot contain a Koebe sequence of arcs provided the order of normality of f is less than a certain positive constant ${C^\ast }$.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 190 (1974), 207-222
  • MSC: Primary 30A72
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0338376-5
  • MathSciNet review: 0338376