Tuesday Seminar of Analysis

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.)
Organizer(s) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

2012/06/26

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Kenichi Ito (Division of Mathematics, University of Tsukuba)
Absence of embedded eigenvalues for the Schr\\"odinger operator on manifold with ends (JAPANESE)
[ Abstract ]
We consider a Riemannian manifold with, at least, one expanding end, and prove the absence of $L^2$-eigenvalues for the Schr\\"odinger operator above some critical value. The critical value is computed from the volume growth rate of the end and the potential behavior at infinity. The end structure is formulated abstractly in terms of some convex function, and the examples include asymptotically Euclidean and hyperbolic ends. The proof consists of a priori superexponential decay estimate for eigenfunctions and the absence of superexponentially decaying eigenfunctions, both of which employs the Mourre-type commutator argument. This talk is based on the recent joint work with E.Skibsted (Aarhus University).