{"paper":{"title":"Frames of exponentials and sub-multitiles in LCA groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Carlos Cabrelli, Carolina Mosquera, Davide Barbieri, Eugenio Hern\\'andez, Peter Luthy, Ursula Molter","submitted_at":"2017-10-09T16:23:09Z","abstract_excerpt":"In this note we investigate the existence of frames of exponentials for $L^2(\\Omega)$ in the setting of LCA groups. Our main result shows that sub-multitiling properties of $\\Omega \\subset \\widehat{G}$ with respect to a uniform lattice $\\Gamma$ of $\\widehat{G}$ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of $\\Gamma$. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03176","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"}