## Decay of magnetic eigenfunctions on asymptotically hyperbolic plane

J. Math. Sci. Univ. Tokyo
Vol. 12 (2005), No. 3, Page 319--347.

SHIRAI, Shin-ichi
Decay of magnetic eigenfunctions on asymptotically hyperbolic plane
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Abstract:
We prove a decay estimate for eigenfunctions of the magnetic Schr\"{o}dinger operator on two dimensional Riemannian manifold $M$. We assume that $M$ is simply connected, rotationally symmetric, and asymptotically hyperbolic. The proof is based on a method developed by S. Nakamura in \cite{Nak1}.

Mathematics Subject Classification (1991): 35P15, 81Q10, 58J50.
Mathematical Reviews Number: MR2192220