Cluster expansion of the resolvent for the Schrödinger operator on non-percolating graphs with applications to Simon–Spencer type theorems and localization
The paper contains a generalization of the well-known 1D results on the absence of the a.c. spectrum ( in the spirit of the Simon–Spencer theorem) and localization to the wide class of “non-percolating” graphs, which include the Sierpiński lattice and quasi 1D trees. The main tools are cluster expan...
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| Veröffentlicht in: | Journal of spectral theory 2017-01, Vol.7 (3), p.733-770 |
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| container_end_page | 770 |
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| container_issue | 3 |
| container_start_page | 733 |
| container_title | Journal of spectral theory |
| container_volume | 7 |
| creator | Molchanov, Stanislav Zheng, Lukun |
| description | The paper contains a generalization of the well-known 1D results on the absence of the a.c. spectrum ( in the spirit of the Simon–Spencer theorem) and localization to the wide class of “non-percolating” graphs, which include the Sierpiński lattice and quasi 1D trees. The main tools are cluster expansion of the resolvent and real analytic techniques (Kolmogorov’s lemma and similar estimates). |
| doi_str_mv | 10.4171/JST/176 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 1664-039X |
| ispartof | Journal of spectral theory, 2017-01, Vol.7 (3), p.733-770 |
| issn | 1664-039X 1664-0403 |
| language | eng |
| recordid | cdi_gale_infotracacademiconefile_A511109532 |
| source | European Mathematical Society Publishing House |
| subjects | Graph theory Mathematical research Polynomials Potential theory Power series Real functions Schrödinger equation |
| title | Cluster expansion of the resolvent for the Schrödinger operator on non-percolating graphs with applications to Simon–Spencer type theorems and localization |
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