## 偏微分方程式セミナー (2014/7/28): Absence of $B_0^*$-eigenfunctions and LAP on manifold with ends, 伊藤健一氏(神戸大学)

2014年 　 7月 28日 17時 00分 ～ 2014年 　 7月 28日 18時 00分

We prove the absence of $B^*_0$-eigenfunctions and the limiting absorption
principle (LAP) for the Schr\"odinger operator on a manifold with Euclidean
and/or hyperbolic ends. Here the function space $B^*_0$ is the completion
of $C^\infty_0(M)$ in the Agmon-H\"ormander space $B^*$, or the Besov
space with respect to the configuration weight. The main tool for the proofs
is the Mourre-type commutator argument. It is known that on hyperbolic
manifolds this argument does not work directly, however we extend it by
carefully designing the modified radii and the associated conjugate
operators.
In the proof of LAP we also introduce an alternative method avoiding energy
cutoffs. This is a joint work with Erik Skibsted, Aarhus University.

（講演開始時刻が通常と異なりますのでご注意ください。）