Andrew Comech Promotion Talk

Date: September 16, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Andrew Comech Promotion Talk, Texas A&M University

Description:

TITLE: Virtual levels

ABSTRACT: Virtual levels admit several equivalent definitions: (1) These are the points of the essential spectrum corresponding to either eigenvectors or to "virtual states", which are functions from a "slightly larger" space; (2) In the vicinity of these points, there is no "limiting absorption principle": the resolvent can not be uniformly bounded in certain weighted spaces; (3) There is a bifurcation of eigenvalues from these points under a perturbation which could be arbitrarily small. As an illustration of our approach, we give an application to the Schrodinger operator in any dimension and with nonselfadjoint potentials, supplementing the approaches by Jensen--Kato (1979), Jensen--Nenciu (2000), and Yafaev (2010).