Scattering the Geometry of Weighted Graphs
- Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal.
| Author details: | Batu GüneysuGND, Matthias KellerORCiD |
|---|---|
| DOI: | https://doi.org/10.1007/s11040-018-9285-1 |
| ISSN: | 1385-0172 |
| ISSN: | 1572-9656 |
| Title of parent work (English): | Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics |
| Publisher: | Springer |
| Place of publishing: | Dordrecht |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2018/09/14 |
| Publication year: | 2018 |
| Release date: | 2021/09/29 |
| Tag: | Graphs; Laplacian; Scattering theory |
| Volume: | 21 |
| Issue: | 3 |
| Number of pages: | 15 |
| Funding institution: | DFGGerman Research Foundation (DFG) |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
