{"paper":{"title":"Characterization of potential smoothness and Riesz basis property of Hill-Scr\\\"odinger operators with singular periodic potentials in terms of periodic, antiperiodic and Neumann spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Ahmet Batal","submitted_at":"2013-09-24T19:16:24Z","abstract_excerpt":"The Hill operators Ly=-y''+v(x)y, considered with singular complex valued \\pi-periodic potentials v of the form v=Q' with Q in L^2([0,\\pi]), and subject to periodic, antiperiodic or Neumann boundary conditions have discrete spectra. For sufficiently large n, the disc {z: |z-n^2|<n} contains two periodic (if n is even) or antiperiodic (if n is odd) eigenvalues \\lambda_n^-, \\lambda_n^+ and one Neumann eigenvalue \\nu_n. We show that rate of decay of the sequence |\\lambda_n^+-\\lambda_n^-|+|\\lambda_n^+ - \\nu_n| determines the potential smoothness, and there is a basis consisting of periodic (or ant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6293","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"}