{"paper":{"title":"Gabor systems and almost periodic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio Galbis, Carmen Fern\\'andez, Paolo Boggiatto","submitted_at":"2014-12-11T09:54:12Z","abstract_excerpt":"We give a construction of Gabor type frames for suitable separable subspaces of the non-separable Hilbert spaces $AP_2({\\mathbb R})$ of almost periodic functions of one variable. Furthermore we determine a non-countable generalized frame for the whole space $AP_2({\\mathbb R}).$ We show furthermore that Bessel-type estimates hold for the $AP$ norm with respect to a countable Gabor system using suitable almost periodic norms of sequencies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3587","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"}