{"paper":{"title":"On the Riesz basis property of root vectors system for $2 \\times 2$ Dirac type operators","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":"2015-04-20T07:22:52Z","abstract_excerpt":"The paper is concerned with the Riesz basis property of a boundary value problem associated in $L^2[0,1] \\otimes \\mathbb{C}^2$ with the following $2 \\times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \\lambda y, \\quad B = \\begin{pmatrix} b_1 & 0 \\\\ 0 & b_2 \\end{pmatrix}, \\quad y = \\begin{pmatrix} y_1 \\\\ y_2 \\end{pmatrix}, \\quad (1) $$ with a summable potential matrix $Q \\in L^1[0,1] \\otimes \\mathbb{C}^{2 \\times 2}$ and $b_1 < 0 < b_2$. If $b_2 = -b_1 =1$ this equation is equivalent to one dimensional Dirac equation. It is proved that the system of root functions of a linear boundary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04954","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"}