BEGIN:VCALENDAR PRODID:-//TAMU Math Calendar//NONSGML v1.0//EN VERSION:2.0 BEGIN:VEVENT DTSTART:20190916T160000Z DTEND:20190916T170000Z SUMMARY:Andrew Comech Promotion Talk DESCRIPTION:
TITLE: Virtual levelsEND:VEVENT END:VCALENDAR
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).