{"paper":{"title":"Knit product of finite groups and sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.FA","authors_text":"Albert Ibort, Antonio G. Garc\\'ia, Miguel A. Hern\\'andez-Medina","submitted_at":"2018-06-28T16:32:02Z","abstract_excerpt":"A finite sampling theory associated with a unitary representation of a finite non Abelian group $\\mathbf{G}$ on a Hilbert space is stablished. The non Abelian group $\\mathbf{G}$ is a knit product $\\mathbf{N}\\bowtie \\mathbf{H}$ of two finite subgroups $\\mathbf{N}$ and $\\mathbf{H}$. Sampling formulas where the samples are indexed by either $\\mathbf{N}$ or $\\mathbf{H}$ are obtained. Using suitable expressions for the involved samples, the problem is reduced to obtain dual frames in the Hilbert space $\\ell^2(\\mathbf{G})$ having a unitary invariance property; this is done by using matrix analysis t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11481","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"}