Eintrag in der Universitätsbibliographie der TU Chemnitz
Volltext zugänglich unter
URN: urn:nbn:de:bsz:ch1-qucosa-102766
Seifert, Christian
Stollmann, Peter (Prof. Dr.) ; Lenz, Daniel (Prof. Dr.) (Gutachter)
Measure-perturbed one-dimensional Schrödinger operators
Kurzfassung in englisch
In this Dissertation thesis the spectral theory of Schrödinger operators modeling quasicrystals in dimension one ist investigated. We allow for a large class of measures as potentials covering also point interactions.The main results can be stated as follows: If the potential can be very well approximated by periodic potentials, then the correspondig Schrödinger operator does not have any eigenvalues. If the potential is aperiodic and satisfies a certain finite local complexity condition, the absolutely continuous spectrum is absent. We also prove Cantor spectra of zero Lebesgue measure for a large class of (a randomized version of) the operator.
| Universität: | Technische Universität Chemnitz | |
| Institut: | Professur Analysis | |
| Fakultät: | Fakultät für Mathematik | |
| Dokumentart: | Dissertation | |
| Betreuer: | Stollmann, Peter (Prof. Dr.) | |
| URL/URN: | http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-102766 | |
| SWD-Schlagwörter: | Hamilton-Operator , Spektraltheorie | |
| Freie Schlagwörter (Deutsch): | Schrödinger Operator , Spektraltheorie , Quasikristalle | |
| Freie Schlagwörter (Englisch): | Schrödinger operator, spectral theory, quasicrystals | |
| DDC-Sachgruppe: | Analysis | |
| Tag der mündlichen Prüfung | 27.11.2012 |
