{"paper":{"title":"Frame set for shifted sinc-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrei V. Semenov, Yurii Belov","submitted_at":"2023-09-12T05:36:20Z","abstract_excerpt":"We prove that frame set $\\mathcal{F}_g$ for imaginary shift of sinc-function $$g(t)=\\frac{\\sin\\pi b(t-iw)}{t-iw}, \\quad b,w\\in\\mathbb{R}\\setminus\\{0\\}$$ can be described as $\\mathcal{F}_g=\\{(\\alpha,\\beta): \\alpha\\beta\\leq 1, \\beta\\leq|b|\\}.$ \\\\ In addition, we prove that $\\mathcal{F}_g=\\{(\\alpha,\\beta): \\alpha\\beta\\leq 1 \\}$ for window functions $g$ of the form $\\frac{1}{t-iw}(1-\\sum\\limits_{k=1}^{\\infty}a_ke^{2\\pi i b_k t})$, such that $\\sum_{k\\geq 1}|a_k|e^{2\\pi|w|b_k}<1$, $wb_k<0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05969","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.05969/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}