# Lukas Schimmer: On the construction of distinguished self-adjoint extensions of operators with gaps

**Time: **
Wed 2019-01-30 17.00 - 18.00

**Lecturer: **
Lukas Schimmer, University of Copenhagen

**Location: ** Seminar Hall Kuskvillan, Institut Mittag-Leffler

Abstract: 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.