A reverse Denjoy theorem II |
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Authors: | P C Fenton J Rossi |
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Institution: | 1.Department of Mathematics and Statisics,University of Otago,Dunedin,New Zealand;2.Department Of Mathematics,Virginia Tech,Blacksburg,USA |
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Abstract: | For α satisfying 0 < α < π, suppose that C
1 and C
2 are rays from the origin, C
1: z = re
i(π−α) and C
2: z = re
i(π+α), r ≥ 0, and that D = {z: | arg z − π| < α}. Let u be a nonconstant subharmonic function in the plane and define B(r, u) = sup|z|=r
u(z) and A
D
(r, u) = $
\inf _{z \in \bar D_r }
$
\inf _{z \in \bar D_r }
u(z), where D
r
= {z: z ∈ D and |z| = r}. If u(z) = (1 + o(1))B(|z|, u) as z → ∞ on C
1 ∪ C
2 and A
D
(r, u) = o(B(r, u)) as r → ∞, then the lower order of u is at least π/(2α). |
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Keywords: | |
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