{"paper":{"title":"An Approximation Problem in Multiplicatively Invariant Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Cabrelli, Carolina A. Mosquera, Victoria Paternostro","submitted_at":"2016-02-27T16:09:39Z","abstract_excerpt":"Let $\\mathcal{H}$ be Hilbert space and $(\\Omega,\\mu)$ a $\\sigma$-finite measure space. Multiplicatively invariant (MI) spaces are closed subspaces of $ L^2(\\Omega, \\mathcal{H})$ that are invariant under point-wise multiplication by functions in a fix subset of $L^{\\infty}(\\Omega).$ Given a finite set of data $\\mathcal{F}\\subseteq L^2(\\Omega, \\mathcal{H}),$ in this paper we prove the existence and construct an MI space $M$ that best fits $\\mathcal{F}$, in the least squares sense. MI spaces are related to shift invariant (SI) spaces via a fiberization map, which allows us to solve an approximati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08608","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"}