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

Tid: To 2019-02-07 kl 14.00 - 15.00

Föreläsare: Lukas Schimmer, University of Copenhagen

Plats: 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.

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Tillhör: Institutionen för matematik
Senast ändrad: 2019-01-31