Andrew Comech (Texas A&M University)
Title: Limiting absorption principle and virtual levels of operators in Banach spaces
Abstract: Virtual levels, also known as threshold resonances, admit several equivalent characterizations:
1. there are corresponding "virtual states" from a space "slightly weaker" than L^2;
2. there is no limiting absorption principle in their vicinity (e.g. no weights such that the "sandwiched" resolvent is uniformly bounded);
3. an arbitrarily small perturbation can produce an eigenvalue.
We develop a general approach to virtual levels in Banach spaces and provide applications to Schroedinger operators with nonselfadjoint potentials and in any dimension, deriving optimal estimates on the resolvent (including the lower dimensional cases).
听
This is a joint work with Nabile Boussaid (Universit茅 Franche-Comte Besan莽on).
听
Zoom link:
Meeting ID: 831 1853 9851
Passcode: 215516