{"paper":{"title":"Unconditional convergence of spectral decompositions of 1D Dirac operators with regular boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Boris Mityagin, Plamen Djakov","submitted_at":"2010-08-24T17:39:35Z","abstract_excerpt":"One dimensional Dirac operators $$ L_{bc}(v) \\, y = i \n\\begin{pmatrix} 1 & 0 \n  0 & -1 \\end{pmatrix} \\frac{dy}{dx} + v(x) y, \\quad y = \\begin{pmatrix} y_1\n  y_2 \\end{pmatrix}, \\quad x\\in[0,\\pi],$$ considered with $L^2$-potentials $ v(x) = \\begin{pmatrix} 0 & P(x)\n  Q(x) & 0 \\end{pmatrix} $ and subject to regular boundary conditions ($bc$), have discrete spectrum.\n  For strictly regular $bc,$ it is shown that every eigenvalue of the free operator $L^0_{bc}$ is simple and has the form $\\lambda_{k,\\alpha}^0 = k + \\tau_\\alpha $ where $ \\; \\alpha \\in \\{1,2\\}, \\; k \\in 2 \\mathbb{Z} $ and $\\tau_\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4095","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"}