Riesz decompositions for Schrödinger operators on graphs
- We study superharmonic functions for Schrodinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into a harmonic and a potential part. The second one decomposes a superharmonic function into a sum of superharmonic functions with certain upper bounds given by prescribed superharmonic functions. As application we show a Brelot type theorem.
| Author details: | Florian Fischer, Matthias KellerORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1016/j.jmaa.2020.124674 |
| ISSN: | 0022-247X |
| ISSN: | 1096-0813 |
| Title of parent work (English): | Journal of mathematical analysis and applications |
| Publisher: | Elsevier |
| Place of publishing: | Amsterdam |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/03/01 |
| Publication year: | 2021 |
| Release date: | 2023/03/09 |
| Tag: | Greatest harmonic minorant; Green's function; Potential theory; Schrödinger operator; Subcritical; Weighted; graph |
| Volume: | 495 |
| Issue: | 1 |
| Article number: | 124674 |
| Number of pages: | 22 |
| Funding institution: | DFG German Research Foundation (DFG)European Commission [KE1841/7-1]; Heinrich-Boll-Stiftung [P139140] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
