{"paper":{"title":"Analysis of the essential spectrum of singular matrix differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Christiane Tretter, Orif O. Ibrogimov, Petr Siegl","submitted_at":"2015-12-02T16:27:02Z","abstract_excerpt":"A complete analysis of the essential spectrum of matrix-differential operators $\\mathcal A$ of the form \\begin{align} \\begin{pmatrix} -\\displaystyle{\\frac{\\rm d}{\\rm d t}} p \\displaystyle{\\frac{\\rm d}{\\rm d t}} + q & -\\displaystyle{\\frac{\\rm d}{\\rm d t}} b^* \\! + c^* \\\\[2mm] \\hspace{6mm} b \\displaystyle{\\frac{\\rm d}{\\rm d t}} + c & \\hspace{4mm} D \\end{pmatrix} \\quad \\text{in } \\ L^2((\\alpha, \\beta)) \\oplus \\bigl(L^2((\\alpha, \\beta))\\bigr)^n \\label{mo} \\end{align} singular at $\\beta\\in\\mathbb R\\cup\\{\\infty\\}$ is given; the coefficient functions $p$, $q$ are scalar real-valued with $p>0$, $b$, $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00759","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"}