Doktorski študij

The course focuses on the extension theory of symmetric operators in Hilbert spaces and its applications to linear differential operators, including Hamiltonians with point interactions, quantum graphs, and elliptic PDEs. The first part of the course will be devoted to the classical approach developed by J. von Neumann, K. Friedrichs, and M. G. Krein. We will then introduce a powerful modern approach to the theory of self-adjoint extensions based on the notion of a boundary triplet for the adjoint of a symmetric operator. Pioneered by J. W. Calkin, M. Vishik, and M. Birman, this approach has proved especially useful in the study of differential operators.