{"paper":{"title":"Quadratic pencil of difference equations: Jost solutions, spectrum, and principal vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Murat Adivar","submitted_at":"2008-09-19T07:48:43Z","abstract_excerpt":"In this paper, a quadratic pencil of Schr\\\"odinger type difference operator $L_{\\lambda}$ is taken under investigation to give a general perspective on the spectral analysis of non-selfadjoint difference equations of second order. Introducing Jost-type solutions, structural and quantitative properties of spectrum of the operator $L_{\\lambda}$ are analyzed and hence, a discrete analog of the theory in Degasperis, (\\emph{J.Math.Phys}. 11: 551--567, 1970) and Bairamov et. al, (\\emph{Quaest. Math.} 26: 15--30, 2003) is developed. In addition, several analogies are established between difference an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3317","kind":"arxiv","version":2},"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"}