- Series
- Math Physics Seminar
- Time
- Thursday, October 3, 2013 - 3:30pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Roger Nichols – University of Tennessee, Chattanooga – roger-nichols@utc.edu
- Organizer
- Evans Harrell
Following Kato, we define the sum, H=H0+V, of two linear operators, H0 and V, in a fixed Hilbert space in terms of its resolvent. In an abstract theorem, we present conditions on V that guarantee dom(H1/20)=dom(H1/2) (under certain sectorality assumptions on H0 and H). Concrete applications to non-self-adjoint Schr\"{o}dinger-type operators--including additive perturbations of uniformly elliptic divergence form partial differential operators by singular complex potentials on domains--where application of the abstract theorem yields dom(H1/2)=dom((H∗)1/2), will be presented. This is based on joint work with Fritz Gesztesy and Steve Hofmann.