The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum
| dc.creator | Brown, Malcolm | |
| dc.creator | Hinchcliffe, James | |
| dc.creator | Marletta, Marco | |
| dc.creator | Naboko, Serguei | |
| dc.creator | Wood, Ian | |
| dc.date | 2008-08-27 | |
| dc.date | 2009-02-09 | |
| dc.date.accessioned | 2026-07-07T12:38:45Z | |
| dc.date.available | 2026-07-07T12:38:45Z | |
| dc.description | In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M-function see the same singularities as the resolvent of a certain restriction $A_B$ of the maximal operator? We obtain results showing that it is possible to describe explicitly certain spaces $\Sc$ and $\tilde{\Sc}$ such that the resolvent bordered by projections onto these subspaces is analytic everywhere that the M-function is analytic. We present three examples -- one involving a Hain-Lüst type operator, one involving a perturbed Friedrichs operator and one involving a simple ordinary differential operators on a half line -- which together indicate that the abstract results are probably best possible. | |
| dc.description | 21 pages minor amendments, extra references | |
| dc.identifier | https://arxiv.org/abs/0808.3733 | |
| dc.identifier | http://arxiv.org/abs/0808.3733 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218869 | |
| dc.subject | Spectral Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J25, 35P05, 47A10, 47A11 | |
| dc.title | The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum | |
| dc.type | text |