{"paper":{"title":"Extra invariance of principal shift invariant spaces and the Zak transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carolina A. Mosquera, Davide Barbieri, Eugenio Hernandez","submitted_at":"2019-04-23T21:08:56Z","abstract_excerpt":"We prove a necessary and sufficient condition for a principal shift invariant space of $L^2(\\mathbb{R})$ to be invariant under translations by the subgroup $\\frac{1}{N} \\mathbb{Z}, N>1$. This condition is given in terms of the Zak transform of the group $\\frac{1}{N} \\mathbb{Z}.$ This result is extended to principal shift invariant spaces generated by a lattice in a general locally compact abelian (LCA) group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10538","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"}