{"paper":{"title":"Data Assimilation and Sampling in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Guergana Petrova, Przemyslaw Wojtaszczyk, Ronald DeVore","submitted_at":"2016-02-19T22:59:27Z","abstract_excerpt":"This paper studies the problem of approximating a function $f$ in a Banach space $X$ from measurements $l_j(f)$, $j=1,\\dots,m$, where the $l_j$ are linear functionals from $X^*$. Most results study this problem for classical Banach spaces $X$ such as the $L_p$ spaces, $1\\le p\\le \\infty$, and for $K$ the unit ball of a smoothness space in $X$. Our interest in this paper is in the model classes $K=K(\\epsilon,V)$, with $\\epsilon>0$ and $V$ a finite dimensional subspace of $X$, which consists of all $f\\in X$ such that $dist(f,V)_X\\le \\epsilon$. These model classes, called {\\it approximation sets},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06342","kind":"arxiv","version":3},"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"}