## 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
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}.