{"paper":{"title":"On integral estimates of non-negative positive definite functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrey Efimov, Marcell Gaal, Szilard Gy. Revesz","submitted_at":"2016-12-01T13:14:12Z","abstract_excerpt":"Let $\\ell>0$ be arbitrary. We introduce the extremal quantities $$ G(\\ell):=\\frac{\\sup_{f} \\int_{-\\ell}^{\\ell} f\\,dx}{\\int_{-1}^1 f\\,dx},\\quad C(\\ell):=\\frac{\\sup_{f} \\sup_{a\\in {\\mathbb R}} \\int_{a-\\ell}^{a+\\ell} f\\,dx}{\\int_{-1}^1 f\\,dx}, $$ where the supremum is taken over all not identically zero non-negative positive definite functions. We are interested in the question: how large can the above extremal quantities be?\n  This problem was originally posed by Yu. Shteinikov and S. Konyagin for the case $\\ell=2$. In this note we obtain exact values for the right limits $G(k+0)$ and $C(k+0)$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00235","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"}