{"paper":{"title":"Orthogonal Polynomials with Recursion Coefficients of Generalized Bounded Variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Milivoje Lukic","submitted_at":"2010-08-23T16:08:05Z","abstract_excerpt":"We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an $\\ell^p$ condition and a generalized bounded variation condition. This latter condition requires that a sequence can be expressed as a sum of sequences $\\beta^{(l)}$, each of which has rotated bounded variation, i.e., $\\sum_{n=0}^\\infty | e^{i\\phi_l} \\beta_{n+1}^{(l)} - \\beta_n^{(l)} |$ is finite for some $\\phi_l$. This includes discrete Schr\\\"odinger operators on a half-line or line with finite linear combinations of Wigner--von Neumann type potentials.\n  For the real line, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3844","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"}