{"paper":{"title":"On pointwise estimates of positive definite functions with given support","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mihail N. Kolountzakis, Szilard Gy. Revesz","submitted_at":"2003-02-17T19:20:03Z","abstract_excerpt":"The following problem originated from a question due to Paul Turan. Suppose $\\Omega$ is a convex body in Euclidean space $\\RR^d$ or in $\\TT^d$, which is symmetric about the origin. Over all positive definite functions supported in $\\Omega$, and with normalized value 1 at the origin, what is the largest possible value of their integral? From this Arestov, Berdysheva and Berens arrived to pose the analogous pointwise extremal problem for intervals in $\\RR$. That is, under the same conditions and normalizations, and for any particular point $z\\in\\Omega$, the supremum of possible function values a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0302193","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"}