{"paper":{"title":"Recovering functions from the Paley-Wiener amalgam space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jeff Ledford","submitted_at":"2013-11-20T18:53:45Z","abstract_excerpt":"In this paper we show that functions from the Paley-Wiener amalgam space $(PW,l^1)=\\{f\\in L^2(\\mathbb{R}): \\sum\\|\\hat{f}(\\xi+2\\pi m) \\|_{L^2([-\\pi,\\pi])} < \\infty\\}$ enjoy similar recovery properties as the classical Paley-Wiener space. Specifically, if $\\{\\phi_\\alpha(x): \\alpha\\in A\\}$ is a regular family of interpolators and $\\{x_n: n\\in \\mathbb{Z}\\}$ is a complete interpolating sequence for $L^2([-\\pi,\\pi])$, then the family $\\{ e^{2\\pi i m x}\\phi_{\\alpha}(x-x_n): m,n\\in \\mathbb{Z}, \\alpha\\in A \\} $ may be used to recover $f\\in(PW,l^1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5169","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"}