{"paper":{"title":"Strong Divergence of Reconstruction Procedures for the Paley-Wiener Space $\\mathcal{PW}^1_\\pi$ and the Hardy Space $\\mathcal{H}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Brendan Farrell, Holger Boche","submitted_at":"2014-04-16T23:33:21Z","abstract_excerpt":"Previous results on certain sampling series have left open if divergence only occurs for certain subsequences or, in fact, in the limit. Here we prove that divergence occurs in the limit.\n  We consider three canonical reconstruction methods for functions in the Paley-Wiener space $\\mathcal{PW}^1_\\pi$. For each of these we prove an instance when the reconstruction diverges in the limit. This is a much stronger statement than previous results that provide only $\\limsup$ divergence. We also address reconstruction for functions in the Hardy space $\\mathcal{H}^1$ and show that for any subsequence o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4400","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"}