{"paper":{"title":"Approximation of analytic functions in Korobov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Friedrich Pillichshammer, Henryk Wo\\'zniakowski, Josef Dick, Peter Kritzer","submitted_at":"2012-11-25T23:46:01Z","abstract_excerpt":"We study multivariate $L_2$-approximation for a weighted Korobov space of analytic periodic functions for which the Fourier coefficients decay exponentially fast. The weights are defined, in particular, in terms of two sequences $\\boldsymbol{a} =\\{a_j\\}$ and $\\boldsymbol{b} =\\{b_j\\}$ of numbers no less than one. Let $e^{L_2-\\mathrm{app},\\Lambda}(n,s)$ be the minimal worst-case error of all algorithms that use $n$ information functionals from the class $\\Lambda$ in the $s$-variate case. We consider two classes $\\Lambda$: the class $\\Lambda^{{\\rm all}}$ consists of all linear functionals and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5822","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"}