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Upper and lower bounds for the best Markov constant $c_{n}(\\lambda)$ are obtained, which are valid for all $n\\in"},"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":"1702.05963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-20T13:42:38Z","cross_cats_sorted":[],"title_canon_sha256":"3611afc4c68f2e648eb98ac8bd9b441cce915b9ad57c97c770ac888529de32f2","abstract_canon_sha256":"ca8d30c38a227092d88de2ed91f95c22d00e87a13b445bb465b7042cdfda8530"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:24.748241Z","signature_b64":"OSZIQ+qWVG3NJ/3le2UGxwpFJScflK7ATqf0+n7heo3BcV0IFMFPexXP+sXP/o20Kgy+mEsTGOzFgX4cFr/fCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28b2952c2977a604b652b114425a10f207f8f4cfe66325b7f32cae3d3d35bb9f","last_reissued_at":"2026-05-18T00:50:24.747554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:24.747554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Markov $L_2$ inequality with the Gegenbauer weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dragomir Aleksov, Geno Nikolov","submitted_at":"2017-02-20T13:42:38Z","abstract_excerpt":"For the Gegenbauer weight function $w_{\\lambda}(t)=(1-t^2)^{\\lambda-1/2}$, $\\lambda>-1/2$, we denote by $\\Vert\\cdot\\Vert_{w_{\\lambda}}$ the associated $L_2$-norm, $$ \\Vert f\\Vert_{w_{\\lambda}}:=\\Big(\\int_{-1}^{1}w_{\\lambda}(t)f^2(t)\\,dt\\Big)^{1/2}. $$ We study the Markov inequality $$ \\Vert p^{\\prime}\\Vert_{w_{\\lambda}}\\leq c_{n}(\\lambda)\\,\\Vert p\\Vert_{w_{\\lambda}},\\qquad p\\in \\mathcal{P}_n, $$ where $\\mathcal{P}_n$ is the class of algebraic polynomials of degree not exceeding $n$. 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