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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.00235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-01T13:14:12Z","cross_cats_sorted":[],"title_canon_sha256":"7a743b0dce89fc420e8ef8fea4fb10e10dcd3eae8e5ca991c914e61d78eea4d3","abstract_canon_sha256":"40de06c8b6163c8b02a714314d1c4e885bacffbde3c78e509b6f4929f5f7d4ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:05.659462Z","signature_b64":"OJ23vuugXC+6Zt/P2mG4ddu/QE5NupOSFH/plkwcP/8xHysa/EVxrHiu3cco0JBm3IQ9PH42UIJvoNxSybdnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e69473b67a011ab10be21dfe69291087165e9896a359bfbbad545dbef51b7c17","last_reissued_at":"2026-05-18T00:56:05.658856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:05.658856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\ell=2$. 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