Self-adjoint curl operators
| dc.creator | Hiptmair, R. | |
| dc.creator | Kotiuga, P. R. | |
| dc.creator | Tordeux, S. | |
| dc.date | 2008-09-04 | |
| dc.date.accessioned | 2026-07-07T10:00:42Z | |
| dc.date.available | 2026-07-07T10:00:42Z | |
| dc.description | We study the exterior derivative as a symmetric unbounded operator on square integrable 1-forms on a 3D bounded domain $D$. We aim to identify boundary conditions that render this operator self-adjoint. By the symplectic version of the Glazman-Krein-Naimark theorem this amounts to identifying complete Lagrangian subspaces of the trace space of H(curl) equipped with a symplectic pairing arising from the $\wedge$-product of 1-forms on $\partial D$. Substantially generalizing earlier results, we characterize Lagrangian subspaces associated with closed and co-closed traces. In the case of non-trivial topology of the domain, different contributions from co-homology spaces also distinguish different self-adjoint extension. Finally, all self-adjoint extensions discussed in the paper are shown to possess a discrete point spectrum, and their relationship with curl curl-operators is discussed. | |
| dc.description | 30 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0809.0826 | |
| dc.identifier | http://arxiv.org/abs/0809.0826 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168395 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47F05, 46N20 | |
| dc.title | Self-adjoint curl operators | |
| dc.type | text |