{"paper":{"title":"Characterization of the potential smoothness of one-dimensional Dirac operator subject to general boundary conditions and its Riesz basis property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"\\.Ilker Arslan","submitted_at":"2016-02-03T13:25:52Z","abstract_excerpt":"The one-dimensional Dirac operator with periodic potential $V=\\begin{pmatrix} 0 & \\mathcal{P}(x) \\\\ \\mathcal{Q}(x) & 0 \\end{pmatrix}$, where $\\mathcal{P},\\mathcal{Q}\\in L^2([0,\\pi])$ subject to periodic, antiperiodic or a general strictly regular boundary condition $(bc)$ has discrete spectrums. It is known that, for large enough $|n|$ in the disc centered at $n$ of radius 1/4, the operator has exactly two (periodic if $n$ is even or antiperiodic if $n$ is odd) eigenvalues $\\lambda_n^+$ and $\\lambda_n^-$ (counted according to multiplicity) and one eigenvalue $\\mu_n^{bc}$ corresponding to the b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01290","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"}