On Self-adjoint and J-self-adjoint Dirac-type Operators: A Case Study
| dc.creator | Clark, Steve | |
| dc.creator | Gesztesy, Fritz | |
| dc.date | 2005-11-15 | |
| dc.date | 2005-11-30 | |
| dc.date.accessioned | 2026-07-07T06:51:15Z | |
| dc.date.available | 2026-07-07T06:51:15Z | |
| dc.description | We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl-Titchmarsh half-line m-coefficients (and 2 x 2 matrix-valued M-matrices) in the non-self-adjoint context and derive some of their basic properties. We conclude with an illustrative example showing that crossing spectral arcs in the non-self-adjoint context imply the blowup of the norm of spectral projections in the limit where the crossing point is approached. | |
| dc.description | 38 pages | |
| dc.identifier | https://arxiv.org/abs/math/0511369 | |
| dc.identifier | http://arxiv.org/abs/math/0511369 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104925 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 34B20; 34B27; 34L40; 34L05; 34L10 | |
| dc.title | On Self-adjoint and J-self-adjoint Dirac-type Operators: A Case Study | |
| dc.type | text |