250110 VO Ausgewählte Kapitel aus Funktionalanalysis (2013S)

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.

Literature:

1. N.I. Akhiezer, I.M. Glazman: Theory of Linear Operators in Hilbert Space.
Ungar, New York (1961).

2. M.A. Naimark: Linear Differential Operators. Ungar, New York (1968).

3. G. Grubb: Distributions and Operators. Springer-Verlag, Berlin (2009).

4. K. Schmuedgen: Unbounded Self-adjoint Operators on Hilbert Space. Springer, (2012).

5. V.A. Derkach, M.M. Malamud: Generalized resolvents and the boundary value problems
for Hermitian operators with gaps. J. Funct. Anal. 95, 1-95 (1991).