{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4Q2FGHIK77Y6TRTLMXTQ3PDIBE","short_pith_number":"pith:4Q2FGHIK","schema_version":"1.0","canonical_sha256":"e434531d0afff1e9c66b65e70dbc680903b8d3733f455dde63a06d2184d43206","source":{"kind":"arxiv","id":"1701.07682","version":1},"attestation_state":"computed","paper":{"title":"On the Markov inequality in the $L_2$-norm with the Gegenbauer weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Shadrin, Geno Nikolov","submitted_at":"2017-01-26T13:15:18Z","abstract_excerpt":"Let $w_{\\lambda}(t) := (1-t^2)^{\\lambda-1/2}$, where $\\lambda > -\\frac{1}{2}$, be the Gegenbauer weight function, let $\\|\\cdot\\|_{w_{\\lambda}}$ be the associated $L_2$-norm, $$\n  \\|f\\|_{w_{\\lambda}} = \\left\\{\\int_{-1}^1 |f(x)|^2 w_{\\lambda}(x)\\,dx\\right\\}^{1/2}\\,, $$ and denote by $\\mathcal{P}_n$ the space of algebraic polynomials of degree $\\le n$.\n  We study the best constant $c_n(\\lambda)$ in the Markov inequality in this norm $$\n  \\|p_n'\\|_{w_{\\lambda}} \\le c_n(\\lambda) \\|p_n\\|_{w_{\\lambda}}\\,,\\qquad p_n \\in \\mathcal{P}_n\\,, $$ namely the constant $$ c_n(\\lambda) := \\sup_{p_n \\in \\mathcal{"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.07682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-26T13:15:18Z","cross_cats_sorted":[],"title_canon_sha256":"bdac44c606ebe860fc0857df39f60154321fc09b3132d6e8b7d2e78896721e19","abstract_canon_sha256":"39bd3a3ad731df19a666ca6bac6d1e45ee20387e0e71e70176d5519e1ba0bccd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.864862Z","signature_b64":"6BCl4EN7uFO63kUWKOApVGvSvcU3x3+8K77R7UxMgVcRQBHkhZ49oE0Zqq6EYSHD0E0LOVFLottrKS+35b1aAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e434531d0afff1e9c66b65e70dbc680903b8d3733f455dde63a06d2184d43206","last_reissued_at":"2026-05-18T00:52:02.864409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.864409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Markov inequality in the $L_2$-norm with the Gegenbauer weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Shadrin, Geno Nikolov","submitted_at":"2017-01-26T13:15:18Z","abstract_excerpt":"Let $w_{\\lambda}(t) := (1-t^2)^{\\lambda-1/2}$, where $\\lambda > -\\frac{1}{2}$, be the Gegenbauer weight function, let $\\|\\cdot\\|_{w_{\\lambda}}$ be the associated $L_2$-norm, $$\n  \\|f\\|_{w_{\\lambda}} = \\left\\{\\int_{-1}^1 |f(x)|^2 w_{\\lambda}(x)\\,dx\\right\\}^{1/2}\\,, $$ and denote by $\\mathcal{P}_n$ the space of algebraic polynomials of degree $\\le n$.\n  We study the best constant $c_n(\\lambda)$ in the Markov inequality in this norm $$\n  \\|p_n'\\|_{w_{\\lambda}} \\le c_n(\\lambda) \\|p_n\\|_{w_{\\lambda}}\\,,\\qquad p_n \\in \\mathcal{P}_n\\,, $$ namely the constant $$ c_n(\\lambda) := \\sup_{p_n \\in 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