{"paper":{"title":"Asymptotic formulas for spectral gaps and deviations of Hill and 1D Dirac 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":"Boris Mityagin, Plamen Djakov","submitted_at":"2013-09-06T19:41:43Z","abstract_excerpt":"Let $L$ be the Hill operator or the one dimensional Dirac operator on the interval $[0,\\pi].$ If $L$ is considered with Dirichlet, periodic or antiperiodic boundary conditions, then the corresponding spectra are discrete and for large enough $|n|$ close to $n^2 $ in the Hill case, or close to $n, \\; n\\in \\mathbb{Z}$ in the Dirac case, there are one Dirichlet eigenvalue $\\mu_n$ and two periodic (if $n$ is even) or antiperiodic (if $n$ is odd) eigenvalues $\\lambda_n^-, \\, \\lambda_n^+ $ (counted with multiplicity).\n  We give estimates for the asymptotics of the spectral gaps $\\gamma_n = \\lambda_n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1751","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"}