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January, 1999 Boundary behavior of positive solutions of Δu=Pu on a Riemann surface
Takeyoshi SATŌ
J. Math. Soc. Japan 51(1): 167-179 (January, 1999). DOI: 10.2969/jmsj/05110167


The classical Fatou limit theorem was extended to the case of positive harmonic functions on a hyperbolic Riemann surface R by Constantinescu-Cornea. They used extensively the notions of Martin's boundary and fine limit following the filter generated by the base of the subsets of R whose complements are closed and thin at a minimal boundary point of R. We shall consider such a problem for positive solutions of the Schrödinger equation on a hyperbolic Riemann surface.


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Takeyoshi SATŌ. "Boundary behavior of positive solutions of Δu=Pu on a Riemann surface." J. Math. Soc. Japan 51 (1) 167 - 179, January, 1999.


Published: January, 1999
First available in Project Euclid: 10 June 2008

zbMATH: 0940.31003
MathSciNet: MR1661016
Digital Object Identifier: 10.2969/jmsj/05110167

Primary: 31A35

Keywords: Fatou limit theorem , fine limit , Martin boundary , Schr\"{o}dinger's equation

Rights: Copyright © 1999 Mathematical Society of Japan

Vol.51 • No. 1 • January, 1999
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