{"paper":{"title":"On the growth of Lebesgue constants for convex polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tetiana Lomako, Yurii Kolomoitsev","submitted_at":"2018-01-02T11:07:14Z","abstract_excerpt":"In the paper, new estimates of the Lebesgue constant $$ \\mathcal{L}(W)=\\frac1{(2\\pi)^d}\\int_{\\mathbb{T}^d}\\bigg|\\sum_{{k}\\in W\\cap \\mathbb{Z}^d} e^{i({k},\\,{x})}\\bigg| {\\rm d}{ x} $$ for convex polyhedra $W\\subset\\mathbb{R}^d$ are obtained. The main result states that if $W$ is a convex polyhedron such that $[0,m_1]\\times\\dots\\times [0,m_d]\\subset W\\subset [0,n_1]\\times\\dots\\times [0,n_d]$, then $$ c(d)\\prod_{j=1}^d \\log(m_j+1)\\le \\mathcal{L}(W)\\le C(d)s\\prod_{j=1}^d \\log(n_j+1), $$ where $s$ is a size of the triangulation of $W$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00608","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"}