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Generalizations of Montel-Lindelöf’s Theorem on Asymptotic Values

Published online by Cambridge University Press:  22 January 2016

Makoto Ohtsuka
Makoto Ohtsuka*
Affiliation:
Mathematical Institute Nagoya University
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Montel [10] proved in 1912 the following theorem: Let w = f(z) be an analytic function in the horizontal strip B : 0 < x < + ∞, 0 < y < 1 (z = x + iy) which is continuous on 0 < x < + ∞, 0 ≦ y < 1 and omits at least two values. If f (x) converges to a value w0 as x → + ∞, then f(z) converges to W0 as z tends to in 0 < x < + ∞, 0 ≦ y < 1 − ε for any ε such that 0 < ε < 1.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 10 , June 1956 , pp. 129 - 163
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1956

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