{"paper":{"title":"Doubling condition at the origin for non-negative positive definite functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitry Gorbachev, Sergey Tikhonov","submitted_at":"2016-12-27T14:03:57Z","abstract_excerpt":"We study upper and lower estimates as well as the asymptotic behavior of the sharp constant $C=C_n(U,V)$ in the doubling-type condition at the origin \\[ \\frac{1}{|V|}\\int_{V}f(x)\\,dx\\le C\\,\\frac{1}{|U|}\\int_{U}f(x)\\,dx, \\] where $U,V\\subset \\mathbb{R}^{n}$ are $0$-symmetric convex bodies and $f$ is a non-negative positive definite function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08637","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"}