{"paper":{"title":"Positivity and Fourier integrals over regular hexagon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yuan Xu","submitted_at":"2015-08-30T18:48:21Z","abstract_excerpt":"Let $f \\in L^1(\\mathbb{R}^2)$ and let $\\widehat f$ be its Fourier integral. We study summability of the partial integral $S_{\\rho,\\mathsf{H}}(x)=\\int_{\\{\\|y\\|_\\mathsf{H} \\le \\rho\\}} e^{i x\\cdot y}\\widehat f(y) dy$, where $\\|y\\|_\\mathsf{H}$ denotes the uniform norm taken over the regular hexagonal domain. We prove that the Riesz $(R,\\delta)$ means of the inverse Fourier integrals are nonnegative if and if $\\delta \\ge 2$. Moreover, we describe a class of $\\|\\cdot\\|_\\mathsf{H}$-radial functions that are positive definite on $\\mathbb{R}^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07615","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"}