Recent developments in the spectral theory for non self-adjoint Hamiltonians
Abstract:
The objective of this survey is to collect and elaborate on different tools, both well-established and more recent ones, which have been developed in the last decades to investigate spectral properties of non-self-adjoint operators of the form $H = H_0 + V$. More specifically, we will show how Hardy-type and Sobolev inequalities, together with Virial theorems and Birman-Schwinger principles enter into play in the analysis of the spectrum of these Hamiltonians.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 11.2022 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000152569 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 27 S. |
| Serie | CRC 1173 Preprint ; 2022/57 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | Spectrum, self-adjoint operators, non self-adjoint operators, Hardy-type inequalities, Mourre theory, Birman-Schwinger principle |