{"paper":{"title":"Riesz bases consisting of root functions of 1D Dirac operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Boris Mityagin, Plamen Djakov","submitted_at":"2011-08-22T01:04:07Z","abstract_excerpt":"For one-dimensional Dirac operators $$ Ly= i \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix} \\frac{dy}{dx} + v y, \\quad v= \\begin{pmatrix} 0 & P \\\\ Q & 0 \\end{pmatrix}, \\;\\; y=\\begin{pmatrix} y_1 \\\\ y_2 \\end{pmatrix}, $$ subject to periodic or antiperiodic boundary conditions, we give necessary and sufficient conditions which guarantee that the system of root functions contains Riesz bases in $L^2 ([0,\\pi], \\mathbb{C}^2).$\n  In particular, if the potential matrix $v$ is skew-symmetric (i.e., $\\overline{Q} =-P$), or more generally if $\\overline{Q} =t P$ for some real $t \\neq 0,$ then there exists"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4225","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"}