{"paper":{"title":"On the existence of orthogonal polynomials for oscillatory weights on a bounded interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hassan Majidian","submitted_at":"2014-04-06T07:12:58Z","abstract_excerpt":"It is shown that the orthogonal polynomials, corresponding to the oscillatory weight $e^{\\im\\omega x}$, exists if $\\omega$ is a transcendental number and $\\tan\\omega/\\omega\\in\\Q$. Also, it is proved that such orthogonal polynomials exist for almost every $\\omega>0$, and the roots are all simple if $\\omega>0$ is either small enough or large enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1551","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"}