{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OI5ZYROKBCOKZDSE4BE2PTGARJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7724faa8b4184686d50b5ebcc6241006c6e4474876aa7a62dfcd263359f9d41a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-24T00:29:37Z","title_canon_sha256":"37ba5f2df305f211d2c6afc2c09c3781a2605cf8204b37a49c3ced1bd3d8defb"},"schema_version":"1.0","source":{"id":"1112.5677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5677","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5677v1","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5677","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"OI5ZYROKBCOK","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OI5ZYROKBCOKZDSE","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OI5ZYROK","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:1cae9f0805c9aa71cbde707b7c6348e61334e50e9e4adf7928a50fc5f37835c8","target":"graph","created_at":"2026-05-18T04:05:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the spaces $A_p(\\mathbb T)$ of functions $f$ on the circle $\\mathbb T$ such that the sequence of Fourier coefficients $\\fu{\\f}=\\{\\fu{\\f}(k), ~k \\in \\mathbb Z\\}$ belongs to $l^p, ~1\\leq p<2$. The norm on $A_p(\\mathbb T)$ is defined by $\\|f\\|_{A_p}=\\|\\fu{\\f}\\nolinebreak\\|_{l^p}$. We study the rate of growth of the norms $\\|e^{i\\lambda\\varphi}\\|_{A_p}$ as $|\\lambda|\\rightarrow \\infty, ~\\lambda\\in\\mathbb R,$ for $C^1$ -smooth real functions $\\varphi$ on $\\mathbb T$. The results have natural applications to the problem on changes of variable in the spaces $A_p(\\mathbb T)$.","authors_text":"Vladimir Lebedev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-24T00:29:37Z","title":"Quantitative estimates in Beurling--Helson type theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5677","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aeaabd5adfe52a3b1b5479223a38103652ab58ed855aa4121fe2e846b2b4aae0","target":"record","created_at":"2026-05-18T04:05:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7724faa8b4184686d50b5ebcc6241006c6e4474876aa7a62dfcd263359f9d41a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-24T00:29:37Z","title_canon_sha256":"37ba5f2df305f211d2c6afc2c09c3781a2605cf8204b37a49c3ced1bd3d8defb"},"schema_version":"1.0","source":{"id":"1112.5677","kind":"arxiv","version":1}},"canonical_sha256":"723b9c45ca089cac8e44e049a7ccc08a5c9e93d2e39acee75bb916924efbdc7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"723b9c45ca089cac8e44e049a7ccc08a5c9e93d2e39acee75bb916924efbdc7f","first_computed_at":"2026-05-18T04:05:37.834799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:37.834799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F1m6AiAeO3vrxyKlJ+St6TQLobgOQ9n+QotjzlEu4AZ+5ph/FXHbpco1XNalOEeAOM2Z7ySWMmHTHH0yEXrCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:37.835146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeaabd5adfe52a3b1b5479223a38103652ab58ed855aa4121fe2e846b2b4aae0","sha256:1cae9f0805c9aa71cbde707b7c6348e61334e50e9e4adf7928a50fc5f37835c8"],"state_sha256":"820a195e4e9a53df75bcde296fdc1c2b58cdc80cb0855fadb6b6da0e724da936"}