Eigenfunctions growth of R-limits on graphs
- A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.
| Author details: | Siegfried BeckusORCiDGND, Latif EliazORCiD |
|---|---|
| DOI: | https://doi.org/10.4171/JST/389 |
| ISSN: | 1664-039X |
| ISSN: | 1664-0403 |
| Title of parent work (English): | Journal of spectral theory / European Mathematical Society |
| Publisher: | EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität |
| Place of publishing: | Berlin |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/12/03 |
| Publication year: | 2021 |
| Release date: | 2023/11/21 |
| Tag: | Essential spectrum; Schrodinger operators; generalized eigenfunctions; graphs; right limits |
| Volume: | 11 |
| Issue: | 4 |
| Number of pages: | 39 |
| First page: | 1895 |
| Last Page: | 1933 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Gold Open-Access |
| DOAJ gelistet | |
| License (German): |  CC-BY - Namensnennung 4.0 International |
