# Absence of $B_0^*$-eigenfunctions and LAP on manifold with ends

Ken-Ichi Ito
(Kobe University)
Analyseseminar
Onsdag, 20 august, 2014, at 15:30-16:30, Koll B3
Abstrakt:

We prove the absence of $B^*_0$-eigenfunctions and
the limiting absorption principle (LAP) for the Schrodinger 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-Hormander 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.

Kontaktperson: Jacob Schach Møller