{"paper":{"title":"Numerical integration of H\\\"older continuous, absolutely convergent Fourier-, Fourier cosine-, and Walsh series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Josef Dick","submitted_at":"2013-12-04T12:22:50Z","abstract_excerpt":"We introduce quasi-Monte Carlo rules for the numerical integration of functions $f$ defined on $[0,1]^s$, $s \\ge 1$, which satisfy the following properties: the Fourier-, Fourier cosine- or Walsh coefficients of $f$ are absolutely summable and $f$ satisfies a H\\\"older condition of order $\\alpha$, for some $0 < \\alpha \\le 1$. We show a convergent rate of the integration error of order $\\max((s-1) N^{-1/2}, s^{\\alpha/2} N^{-\\alpha} )$. The construction of the quadrature points is explicit and is based on Weil sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1135","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"}