Harmonic functions on finitely sheeted unlimited covering surfaces
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- Masaoka Hiroaki MASAOKA Hiroaki
- Department of Mathematics Faculty of Science
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- Segawa Shigeo SEGAWA Shigeo
- Department of Mathematics Daido Institute of Technology
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Author(s)
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- Masaoka Hiroaki MASAOKA Hiroaki
- Department of Mathematics Faculty of Science
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- Segawa Shigeo SEGAWA Shigeo
- Department of Mathematics Daido Institute of Technology
Abstract
We denote by HP(R) and (HB(R), resp.) the class of positive (bounded, resp.) harmonic functions on a Riemann surface R. Consider an open Riemann surface W possessing a Green's function and a p-sheeted ( 1<p<∞) unlimited covering surface ˜{W} of W with projection map \varphi. We give a necessary and sufficient condition, in terms of Martin boundary, for HX(W)\circ\varphi=HX(˜{W})(X=P, B). We also give some examples illustrating the above result when W is the unit disc.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 55(2), 323-334, 2003-04-01
The Mathematical Society of Japan
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