{"paper":{"title":"The Zak transform and the structure of spaces invariant by the action of an LCA group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.FA","authors_text":"Davide Barbieri, Eugenio Hern\\'andez, Victoria Paternostro","submitted_at":"2014-10-27T14:23:02Z","abstract_excerpt":"We study closed subspaces of $L^2(X)$, where $(X, \\mu)$ is a $\\sigma$-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group $\\Gamma$ on $X$. We provide a complete description for these spaces in terms of range functions and a suitable generalized Zak transform. As an application of our main result, we prove a characterization of frames and Riesz sequences in $L^2(X)$ generated by the action of the unitary representation under consideration on a countable set of functions in $L^2(X)$. Finally, closed subspac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7250","kind":"arxiv","version":2},"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"}