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We study the best constant $c_n(\\alpha)$ in the Markov inequality in this norm, $$ | p^{\\prime}|_{w_\\alpha}\\leq c_n(\\alpha)\\,| p|_{w_\\alpha}\\,,\\quad p\\in {\\cal P}_n\\,, $$ namely the constant $$ c_{n}(\\alpha)=\\sup_{\\mathop{}^{p\\in {\\cal P}_n}_{p\\ne 0}}\\frac{| p^{\\prime}|_{w_\\alpha"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.02508","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-09T10:31:19Z","cross_cats_sorted":[],"title_canon_sha256":"60134d4a206bf32f64eb02e728ec1f34bcb61e4f41a9d9093a78957fabda1908","abstract_canon_sha256":"a677b6eb3b70aad6b06033e787d84f1f764f16221eb1456d2649e1a440f748d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:16.362940Z","signature_b64":"XjPW5Roe9+kcwtRvGc8CDXv3LKFaOQ9eUchlj34iKUtypuqdE+niV33Dns3O6FeITPQS46B9sLn7XJbwJuniAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"599de8299011fe307744afd7a3d88934162bb77fb91f958657c1dec63ebe23b2","last_reissued_at":"2026-05-18T01:15:16.362299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:16.362299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $L_2$ Markov Inequality with Laguerre Weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Shadrin, Geno Nikolov","submitted_at":"2016-05-09T10:31:19Z","abstract_excerpt":"Let $w_{\\alpha}(t)=t^{\\alpha}\\,e^{-t}$, $\\alpha>-1$, be the Laguerre weight function, and $|\\cdot|_{w_\\alpha}$ denote the associated $L_2$-norm, i.e., $$ | f|_{w_\\alpha}:=\\Big(\\int_{0}^{\\infty}w_{\\alpha}(t)| f(t)|^2\\,dt\\Big)^{1/2}. $$ Denote by ${\\cal P}_n$ the set of algebraic polynomials of degree not exceeding $n$. We study the best constant $c_n(\\alpha)$ in the Markov inequality in this norm, $$ | p^{\\prime}|_{w_\\alpha}\\leq c_n(\\alpha)\\,| p|_{w_\\alpha}\\,,\\quad p\\in {\\cal P}_n\\,, $$ namely the constant $$ c_{n}(\\alpha)=\\sup_{\\mathop{}^{p\\in {\\cal P}_n}_{p\\ne 0}}\\frac{| p^{\\prime}|_{w_\\alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02508","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.02508","created_at":"2026-05-18T01:15:16.362429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.02508v1","created_at":"2026-05-18T01:15:16.362429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02508","created_at":"2026-05-18T01:15:16.362429+00:00"},{"alias_kind":"pith_short_12","alias_value":"LGO6QKMQCH7D","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LGO6QKMQCH7DA52E","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LGO6QKMQ","created_at":"2026-05-18T12:30:29.479603+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ","json":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ.json","graph_json":"https://pith.science/api/pith-number/LGO6QKMQCH7DA52EV7L2HWEJGQ/graph.json","events_json":"https://pith.science/api/pith-number/LGO6QKMQCH7DA52EV7L2HWEJGQ/events.json","paper":"https://pith.science/paper/LGO6QKMQ"},"agent_actions":{"view_html":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ","download_json":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ.json","view_paper":"https://pith.science/paper/LGO6QKMQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.02508&json=true","fetch_graph":"https://pith.science/api/pith-number/LGO6QKMQCH7DA52EV7L2HWEJGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/LGO6QKMQCH7DA52EV7L2HWEJGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ/action/storage_attestation","attest_author":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ/action/author_attestation","sign_citation":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ/action/citation_signature","submit_replication":"https://pith.science/pith/LGO6QKMQCH7DA52EV7L2HWEJGQ/action/replication_record"}},"created_at":"2026-05-18T01:15:16.362429+00:00","updated_at":"2026-05-18T01:15:16.362429+00:00"}