{"paper":{"title":"Tractability of Multivariate Approximation Defined over Hilbert Spaces with Exponential Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian Irrgeher, Friedrich Pillichshammer, Henryk Wozniakowski, Peter Kritzer","submitted_at":"2015-02-11T12:50:33Z","abstract_excerpt":"We study multivariate approximation defined over tensor product Hilbert spaces. The domain space is a weighted tensor product Hilbert space with exponential weights which depend on two sequences $\\boldsymbol{a}=\\{a_j\\}_{j\\in\\mathbb{N}}$ and $\\boldsymbol{b}=\\{b_j\\}_{j\\in\\mathbb{N}}$ of positive numbers, and on a bounded sequence of positive integers $\\boldsymbol{m}=\\{m_j\\}_{j\\in\\mathbb{N}}$. The sequence $\\boldsymbol{a}$ is non-decreasing and the sequence $\\boldsymbol{b}$ is bounded from below by a positive number. We find necessary and sufficient conditions on $\\boldsymbol{a},\\boldsymbol{b}$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03286","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"}