Friedrichs Extension and Min–Max Principle for Operators with a Gap

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. The eigenvalues of the Friedrichs extension are given by a variational principle that involves only the domain of the symmetric operator. Although Dirac operators describing relativistic particles are not semibounded, the Dirac operator with Coulomb potential is known to have a distinguished extension. Similarly, for Dirac-type operators on manifolds with a boundary a distinguished self-adjoint extension is characterised by the Atiyah-PatodiSinger boundary condition. In this paper, we relate these extensions to a generalisation of the Friedrichs extension to the setting of operators satisfying a gap condition. In addition, we prove, in the general setting, that the eigenvalues of this extension are also given by a variational principle that involves only the domain of the symmetric operator. We also clarify what we believe to be inaccuracies in the existing literature.
OriginalsprogEngelsk
TidsskriftAnnales Henri Poincare
Vol/bind21
Udgave nummer2
Sider (fra-til)327-357
ISSN1424-0637
DOI
StatusUdgivet - 1 feb. 2020

ID: 236317096