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 FischerORCiDGND, Matthias KellerORCiDGND |
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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 |