Friday, December 21, 2018 - 14:15 in D5-153
Virtual levels, zero-energy resonances, properties of virtual states, and the limiting absorption principle near thresholds
A talk in the Oberseminar Analysis series by
Andrew Comech
| Abstract: |
The virtual levels, also known as the threshold resonances and zero energy resonances, admit several equivalent definitions:
(1) there are corresponding virtual states from the space slightly larger than L2;
(2) absence of the limiting absorption principle in the vicinity of the threshold point;
(3) bifurcation of eigenvalues from thresholds under a small perturbation.
We prove the equivalence of these definitions and study properties of corresponding virtual states. Once there is no virtual level, we study the limiting absorption principle near the threshold points, proving that, in the vicinity of a threshold, the resolvent is uniformly bounded in particular weighted spaces. We apply the theory to the Schroedinger operators, although the approach works for general non-selfadjoint operators (and in arbitrary dimension).
This is a joint work with Nabile Boussaid (Besançon) and Fritz Gesztesy (Baylor).
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