Selected topics in Analysis:Extension Theory and Its Applications,
Location and date:
Seminarraum 9, OMP 1, 2nd Floor,
The main focus is on the extension theory of symmetric operators in Hilbert spaces with applications to linear differential operators
(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.
Then we shall proceed with a new powerful approach to the self-adjoint extension theory based on the notion of a boundary triplet for the adjoint of a symmetric operator. Pioneered by M. Vishik and M. Birman, this approach turned out to be especially useful for differential operators.
My lecture notes are available on request.
- 1. K. Schmuedgen: Unbounded Self-adjoint Operators on Hilbert Space. Springer, (2012).
- 2. G. Grubb: Distributions and Operators. Springer-Verlag, Berlin (2009).