Journal of the Mathematical Society of Japan

Boundary behavior of positive solutions of Δu=Pu on a Riemann surface

Takeyoshi SATŌ

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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.

Article information

J. Math. Soc. Japan, Volume 51, Number 1 (1999), 167-179.

First available in Project Euclid: 10 June 2008

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Zentralblatt MATH identifier

Primary: 31A35: Connections with differential equations

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


SATŌ, Takeyoshi. Boundary behavior of positive solutions of $\Delta u=Pu$ on a Riemann surface. J. Math. Soc. Japan 51 (1999), no. 1, 167--179. doi:10.2969/jmsj/05110167.

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