{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6H7XOSC7XTWGFPXTINAIYR6DZD","short_pith_number":"pith:6H7XOSC7","schema_version":"1.0","canonical_sha256":"f1ff77485fbcec62bef343408c47c3c8f7eb286d9631d84cd7e51c5b84d2ef9a","source":{"kind":"arxiv","id":"1808.05936","version":2},"attestation_state":"computed","paper":{"title":"Szeg\\H{o}'s Condition on Compact subsets of $\\mathbb{C}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"G\\\"okalp Alpan","submitted_at":"2018-08-17T17:29:22Z","abstract_excerpt":"Let $K$ be a non-polar compact subset of $\\mathbb{C}$ and $\\mu_K$ be its equilibrium measure. Let $\\mu$ be a unit Borel measure supported on a compact set which contains the support of $\\mu_K$. We prove that a Szeg\\H{o} condition in terms of the Radon-Nikodym derivative of $\\mu$ with respect to $\\mu_K$ implies that $$\\inf_n \\frac{\\|P_n(\\cdot;\\mu)\\|_{L^2(\\mathbb{C};\\mu)}}{\\mathrm{Cap}(K)^n}>0.$$\n  We show that $\\frac{\\|P_n(\\cdot;\\mu_K)\\|_{L^2(\\mathbb{C};\\mu_K)}}{\\mathrm{Cap}(K)^n}\\geq 1$ for any compact non-polar set $K$. We also prove that under an additional assumption, unboundedness of the s"},"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":"1808.05936","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-08-17T17:29:22Z","cross_cats_sorted":[],"title_canon_sha256":"f96809cf0d6f49dc89242252c80b5cd559f0b744d77c89c598b95a942812b844","abstract_canon_sha256":"643f435dd4f17b8937d18c4b05bc878b8c08a1df4c268bbc767eeb42fcb98efd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:29.759798Z","signature_b64":"tZUuI7gi9NfH5fuHtXGICmro5EcPT4MPqOpOod0dtby4zEBiCnLz9w2CNanbeocfrJ8cpkSLYvh6isOHuNvQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1ff77485fbcec62bef343408c47c3c8f7eb286d9631d84cd7e51c5b84d2ef9a","last_reissued_at":"2026-05-18T00:00:29.759373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:29.759373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Szeg\\H{o}'s Condition on Compact subsets of $\\mathbb{C}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"G\\\"okalp Alpan","submitted_at":"2018-08-17T17:29:22Z","abstract_excerpt":"Let $K$ be a non-polar compact subset of $\\mathbb{C}$ and $\\mu_K$ be its equilibrium measure. Let $\\mu$ be a unit Borel measure supported on a compact set which contains the support of $\\mu_K$. We prove that a Szeg\\H{o} condition in terms of the Radon-Nikodym derivative of $\\mu$ with respect to $\\mu_K$ implies that $$\\inf_n \\frac{\\|P_n(\\cdot;\\mu)\\|_{L^2(\\mathbb{C};\\mu)}}{\\mathrm{Cap}(K)^n}>0.$$\n  We show that $\\frac{\\|P_n(\\cdot;\\mu_K)\\|_{L^2(\\mathbb{C};\\mu_K)}}{\\mathrm{Cap}(K)^n}\\geq 1$ for any compact non-polar set $K$. We also prove that under an additional assumption, unboundedness of the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05936","kind":"arxiv","version":2},"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":"1808.05936","created_at":"2026-05-18T00:00:29.759440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.05936v2","created_at":"2026-05-18T00:00:29.759440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05936","created_at":"2026-05-18T00:00:29.759440+00:00"},{"alias_kind":"pith_short_12","alias_value":"6H7XOSC7XTWG","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6H7XOSC7XTWGFPXT","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6H7XOSC7","created_at":"2026-05-18T12:32:08.215937+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/6H7XOSC7XTWGFPXTINAIYR6DZD","json":"https://pith.science/pith/6H7XOSC7XTWGFPXTINAIYR6DZD.json","graph_json":"https://pith.science/api/pith-number/6H7XOSC7XTWGFPXTINAIYR6DZD/graph.json","events_json":"https://pith.science/api/pith-number/6H7XOSC7XTWGFPXTINAIYR6DZD/events.json","paper":"https://pith.science/paper/6H7XOSC7"},"agent_actions":{"view_html":"https://pith.science/pith/6H7XOSC7XTWGFPXTINAIYR6DZD","download_json":"https://pith.science/pith/6H7XOSC7XTWGFPXTINAIYR6DZD.json","view_paper":"https://pith.science/paper/6H7XOSC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.05936&json=true","fetch_graph":"https://pith.science/api/pith-number/6H7XOSC7XTWGFPXTINAIYR6DZD/graph.json","fetch_events":"https://pith.science/api/pith-number/6H7XOSC7XTWGFPXTINAIYR6DZD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6H7XOSC7XTWGFPXTINAIYR6DZD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6H7XOSC7XTWGFPXTINAIYR6DZD/action/storage_attestation","attest_author":"https://pith.science/pith/6H7XOSC7XTWGFPXTINAIYR6DZD/action/author_attestation","sign_citation":"https://pith.science/pith/6H7XOSC7XTWGFPXTINAIYR6DZD/action/citation_signature","submit_replication":"https://pith.science/pith/6H7XOSC7XTWGFPXTINAIYR6DZD/action/replication_record"}},"created_at":"2026-05-18T00:00:29.759440+00:00","updated_at":"2026-05-18T00:00:29.759440+00:00"}