{"paper":{"title":"Essential spectrum of non-self-adjoint singular matrix differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Orif O. Ibrogimov","submitted_at":"2016-12-15T19:04:23Z","abstract_excerpt":"The purpose of this paper is to study the essential spectrum of non-self-adjoint singular matrix differential operators in the Hilbert space $L^2(\\mathbb{R})\\oplus L^2(\\mathbb{R})$ induced by matrix differential expressions of the form \\begin{align}\\label{abstract:mdo} \\left(\\begin{array}{cc} \\tau_{11}(\\,\\cdot\\,,D) & \\tau_{12}(\\,\\cdot\\,,D)\\\\[3.5ex] \\tau_{21}(\\,\\cdot\\,,D) & \\tau_{22}(\\,\\cdot\\,,D) \\end{array}\\right), \\end{align} where $\\tau_{11}$, $\\tau_{12}$, $\\tau_{21}$, $\\tau_{22}$ are respectively $m$-th, $n$-th, $k$-th and 0 order ordinary differential expressions with $m=n+k$ being even. U"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05193","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"}