Friedrichs Extension and Min–Max Principle for Operators with a Gap
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
---|---|
Journal | Annales Henri Poincare |
Volume | 21 |
Issue number | 2 |
Pages (from-to) | 327-357 |
ISSN | 1424-0637 |
DOIs | |
Publication status | Published - 1 Feb 2020 |
Links
- https://arxiv.org/pdf/1806.05206.pdf
Accepted author manuscript
ID: 236317096