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Positive harmonic functions of finite order in a Denjoy type domain

Author: Hiroaki Aikawa
Journal: Proc. Amer. Math. Soc. 131 (2003), 3873-3881
MSC (2000): Primary 31A05, 31B05, 31B25
Published electronically: April 24, 2003
MathSciNet review: 1999936
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Abstract: We introduce a Denjoy type domain and prove that the dimension of the cone of positive harmonic functions of finite order in the domain with vanishing boundary values is one or two, whenever the boundary is included in a certain set.

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Additional Information

Hiroaki Aikawa
Affiliation: Department of Mathematics, Shimane University, Matsue 690-8504, Japan

Keywords: Denjoy type domain, harmonic function, finite order
Received by editor(s): May 31, 2002
Received by editor(s) in revised form: August 6, 2002
Published electronically: April 24, 2003
Additional Notes: This work was supported in part by Grant-in-Aid for Scientific Research (A) (No. 11304008), (B) (No. 12440040) and Exploratory Research (No. 13874023) Japan Society for the Promotion of Science.
Dedicated: Dedicated to Professor Kaoru Hatano on the occasion of his 60th birthday
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2003 American Mathematical Society

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