Basis Properties of the Eigensystem of non-self-adjoint Operators (23rit099)


(Graz University of Technology)

Boris Mityagin (Ohio State University)


The Banff International Research Station will host the "Basis Properties of the Eigensystem of non-self-adjoint Operators" workshop in Banff from August 20 to September 3, 2023.

One aspect of non-self-adjoint spectral theory focuses on the properties of the eigensystem (eigenvectors and root vectors) of operators $T$ with compact resolvent. In the classical case, when $T$ is assumed to be self-adjoint or normal, the eigenvectors form an orthonormal basis. This fact is frequently used in further applications, for instance in the analysis of differential operators or in quantum theory. However, the basis properties of the eigensystem can be lost when a self-adjoint operator is perturbed by a non-symmetric term. Deciding whether a perturbation preserves the basis properties of the eigensystem or not appears to be a delicate issue, which requires careful and deep analysis of the problem. For instance, in applications in differential operators, precise asymptotic estimates of eigenfunctions of the unperturbed operator and of the size of the perturbation are needed.

This Research in Teams aims at exploring the new ideas in characterizing perturbations which preserve the basis properties and, on the other hand, at constructing perturbations of specific differential operators that break the basis property.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta's Advanced Education and Technology.