Заседание семинара кафедры высшей математики и математической физики состоится 24 марта (среда) в 18-30.

Докладчик: Andrew Comech, Texas A&M University, College Station, TX and IITP, Moscow

Тема: Virtual levels and virtual states of operators in Banach spaces

Абстракт:
Virtual levels admit several equivalent characterizations:
(1) there are corresponding eigenstates from L2 or a space “slightly weaker” than L2;
(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 nonselfadjoint potentials and in any dimension.

This is a joint work with Nabile Boussaid based on the preprint arXiv:2101.11979 [math.AP].

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