{"paper":{"title":"Completeness property of one-dimensional perturbations of normal and spectral operators generated by first order systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Anton A. Lunyov, Mark M. Malamud","submitted_at":"2018-07-14T07:19:41Z","abstract_excerpt":"The paper is concerned with completeness property of rank one perturbations of unperturbed operators generated by special boundary value problems (BVP) for the following $2 \\times 2$ system \\begin{equation}\n  L y = -i B^{-1} y' + Q(x) y = \\lambda y , \\quad\n  B = \\begin{pmatrix} b_1 & 0 \\\\ 0 & b_2 \\end{pmatrix}, \\quad\n  y = \\begin{pmatrix} y_1 \\\\ y_2 \\end{pmatrix}, \\end{equation}\n  on a finite interval assuming that a potential matrix $Q$ is summable, and $b_1 b_2^{-1} \\notin \\mathbb{R}$ (essentially non-Dirac type case). We assume that unperturbed operator generated by a BVP belongs to one of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05345","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"}