Seminar

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.
Organizers
Søren Fournais
Aarhus University
Rupert Frank
LMU Munich
Benjamin Schlein
University of Zurich, UZH
Simone Warzel
TU Munich

Program
Contact

Rupert Frank

frank@math.lmu.de

Other
information

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