{"paper":{"title":"Threshold phenomenon for a family of the Generalized Generalized Friedrichs models with the perturbation of rank one","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.AP","math.DS","math.FA","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Maslina Darus, Saidakhmat N. Lakaev, Said T. Dustov","submitted_at":"2014-11-28T06:24:36Z","abstract_excerpt":"A family $H_\\mu(p),$ $\\mu>0,$ $p\\in\\T^3$ of the Generalized Firedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the three dimensional lattice $\\mathbb{\\Z}^3,$ is considered. The existence or absence of the unique eigenvalue of the operator $H_\\mu(p)$ lying outside the essential spectrum, depending on the values of $\\mu>0$ and $p\\in U_{\\delta}(p_{\\,0})\\subset\\T^3$ is proven. Moreover, the analyticity of associated eigenfunction is shown."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0598","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}