{"paper":{"title":"Reproducing pairs and the continuous nonstationary Gabor transform on LCA groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael Speckbacher, Peter Balazs","submitted_at":"2015-05-27T14:35:44Z","abstract_excerpt":"In this paper we introduce and investigate the concept of repro- ducing pairs as a generalization of continuous frames. Reproducing pairs yield a bounded analysis and synthesis process while the frame condition can be omitted at both stages. Moreover, we will investigate certain continuous frames (resp. reproducing pairs) on LCA groups, which can be described as a continuous version of nonstationary Ga- bor systems and state sufficient conditions for these systems to form a continuous frame (resp. reproducing pair). As a byproduct we iden- tify the structure of the frame operator (resp. resolu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07344","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"}