Boundary behavior of positive solutions of 〓u=Pu on a Riemann surface
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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.
- Tokyo Sugaku Kaisya Zasshi
Tokyo Sugaku Kaisya Zasshi 51(1), 167-179, 1999-01
The Mathematical Society of Japan