{"paper":{"title":"On the completeness of the system of root vectors for first-order systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"L.L. Oridoroga, M.M. Malamud","submitted_at":"2011-09-16T18:15:50Z","abstract_excerpt":"The paper is concerned with the completeness problem of root functions of general boundary value problems for first order systems of ordinary differential equations. Namely, we introduce and investigate the class of \\emph{weakly regular boundary conditions}. We show that this class is much broader than the class of {\\em regular boundary conditions} introduced by G.D. Birkhoff and R.E. Langer. Our main result states that the system of root functions of a boundary value problem is complete and minimal provided that the boundary conditions are weakly regular. Moreover, we show that in some cases "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3683","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"}