{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UF6ESIZG37P5QMUFRSWVXYF4T6","short_pith_number":"pith:UF6ESIZG","schema_version":"1.0","canonical_sha256":"a17c492326dfdfd832858cad5be0bc9f9ea29f8ce048d53519f0f5a164dd7a87","source":{"kind":"arxiv","id":"1307.0623","version":1},"attestation_state":"computed","paper":{"title":"On the Interpolation of Analytic Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.A. Shkalikov, A.M. Savchuk","submitted_at":"2013-07-02T08:33:43Z","abstract_excerpt":"Let (E_0,E_1) and (H_0,H_1) be a pair of Banach spaces with dense and continuous embeddings E_1 into E_0, H_1 into H_0. For $\\theta \\in [0,1]$ denote by $B_\\theta(0,R)$ the ball of radius R centered at zero in the interpolation spaces E_\\theta. Assume that an analytic map $\\Phi$ maps the ball B_0(0,R) into H_0, $\\Phi$ maps B_1(0,R) into H_1 and for $\\theta =0,1$ the estimates $$ \\|\\Phi(x)\\|_{H_\\theta} \\le C_\\theta\\|x\\|_{H_\\theta}, \\forall\\ x\\in B_\\theta(0,R), $$ hold. Then for all $\\theta\\in(0, 1)$ and r<R $\\Phi$ maps the ball $B_\\theta (0,r)$ into $H_\\theta$ and the same estimate holds for $x"},"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":"1307.0623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-07-02T08:33:43Z","cross_cats_sorted":[],"title_canon_sha256":"e4ce7aef123b161d53b48f3352fff711fa41a9a8d162f7e532a023120a3c8a24","abstract_canon_sha256":"76cc6f4d4fc8e30bec4e3cb0105ebb453325dc7e7af3d1f8fa6492343a49f175"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:25.095039Z","signature_b64":"x2j1K8LzZt0zeZkRtrWwlPQib0R7Rv3u+c+NK7O1m9IK6mFLh/WlCO48ZUncP1dSQM2bZtjOSTQRIbP2BiySDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a17c492326dfdfd832858cad5be0bc9f9ea29f8ce048d53519f0f5a164dd7a87","last_reissued_at":"2026-05-18T03:19:25.094292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:25.094292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Interpolation of Analytic Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.A. Shkalikov, A.M. Savchuk","submitted_at":"2013-07-02T08:33:43Z","abstract_excerpt":"Let (E_0,E_1) and (H_0,H_1) be a pair of Banach spaces with dense and continuous embeddings E_1 into E_0, H_1 into H_0. For $\\theta \\in [0,1]$ denote by $B_\\theta(0,R)$ the ball of radius R centered at zero in the interpolation spaces E_\\theta. Assume that an analytic map $\\Phi$ maps the ball B_0(0,R) into H_0, $\\Phi$ maps B_1(0,R) into H_1 and for $\\theta =0,1$ the estimates $$ \\|\\Phi(x)\\|_{H_\\theta} \\le C_\\theta\\|x\\|_{H_\\theta}, \\forall\\ x\\in B_\\theta(0,R), $$ hold. Then for all $\\theta\\in(0, 1)$ and r<R $\\Phi$ maps the ball $B_\\theta (0,r)$ into $H_\\theta$ and the same estimate holds for $x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0623","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":"1307.0623","created_at":"2026-05-18T03:19:25.094410+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.0623v1","created_at":"2026-05-18T03:19:25.094410+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0623","created_at":"2026-05-18T03:19:25.094410+00:00"},{"alias_kind":"pith_short_12","alias_value":"UF6ESIZG37P5","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UF6ESIZG37P5QMUF","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UF6ESIZG","created_at":"2026-05-18T12:28:02.375192+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/UF6ESIZG37P5QMUFRSWVXYF4T6","json":"https://pith.science/pith/UF6ESIZG37P5QMUFRSWVXYF4T6.json","graph_json":"https://pith.science/api/pith-number/UF6ESIZG37P5QMUFRSWVXYF4T6/graph.json","events_json":"https://pith.science/api/pith-number/UF6ESIZG37P5QMUFRSWVXYF4T6/events.json","paper":"https://pith.science/paper/UF6ESIZG"},"agent_actions":{"view_html":"https://pith.science/pith/UF6ESIZG37P5QMUFRSWVXYF4T6","download_json":"https://pith.science/pith/UF6ESIZG37P5QMUFRSWVXYF4T6.json","view_paper":"https://pith.science/paper/UF6ESIZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.0623&json=true","fetch_graph":"https://pith.science/api/pith-number/UF6ESIZG37P5QMUFRSWVXYF4T6/graph.json","fetch_events":"https://pith.science/api/pith-number/UF6ESIZG37P5QMUFRSWVXYF4T6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UF6ESIZG37P5QMUFRSWVXYF4T6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UF6ESIZG37P5QMUFRSWVXYF4T6/action/storage_attestation","attest_author":"https://pith.science/pith/UF6ESIZG37P5QMUFRSWVXYF4T6/action/author_attestation","sign_citation":"https://pith.science/pith/UF6ESIZG37P5QMUFRSWVXYF4T6/action/citation_signature","submit_replication":"https://pith.science/pith/UF6ESIZG37P5QMUFRSWVXYF4T6/action/replication_record"}},"created_at":"2026-05-18T03:19:25.094410+00:00","updated_at":"2026-05-18T03:19:25.094410+00:00"}