Virtual levels and virtual states of operators in Banach spaces.

Abstract: Virtual levels admit several equivalent characterizations:
(1) there are corresponding eigenstates from L^{^2} or a space “slightly weaker” than L^{^2};
(2) there is no limiting absorption principle in the vicinity of a virtual level (e.g. no weights such that the “sandwiched” resolvent remains 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 non selfadjoint potentials and in any dimension.

Posted on Mar 22, 2021 in Differential Equations, Seminars