On the construction of distinguished self-adjoint extensions of operators with gaps
Spectral Methods in Mathematical Physics
07 February 14:00 - 15:00
Lukas Schimmer - University of Copenhagen
Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. Its eigenvalues are given by a variational principle that involves only the domain of the symmetric operator. Although Dirac operators are not semibounded, the Dirac operator with Coulomb potential is known to have a distinguished self-adjoint extension. Similarly, for Dirac-type operators on manifolds with boundary a distinguished self-adjoint extension is characterised by the Atiyah–Patodi–Singer boundary condition.
At the kick-off conference I related these extensions to a generalisation of the Friedrichs extension to the setting of symmetric operators satisfying a gap condition. In this seminar talk I will present the detailed construction of this extension and will prove that its eigenvalues are also given by a variational principle that involves only the domain of the symmetric operator. This is joint work with Jan Philip Solovej and Sabiha Tokus.
University of Zurich, UZH