{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TM4UHKAJ6WQ47PNAX3JOWPRDXD","short_pith_number":"pith:TM4UHKAJ","schema_version":"1.0","canonical_sha256":"9b3943a809f5a1cfbda0bed2eb3e23b8d44bdac255c4e3c7282affdb584f654b","source":{"kind":"arxiv","id":"1904.12836","version":1},"attestation_state":"computed","paper":{"title":"A linear topological invariant for spaces of quasianalytic functions of Roumieu type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Debrouwere","submitted_at":"2019-04-29T17:38:05Z","abstract_excerpt":"We show that the spaces $\\mathcal{E}_{\\{\\omega\\}}(\\Omega)$ of ultradifferentiable functions of Roumieu type satisfy the dual interpolation estimate for small theta, where $\\omega$ is a quasianalytic weight function and $\\Omega$ is an arbitrary open subset of $\\mathbb{R}^d$. This result was previously shown by Bonet and Doma\\'nski [2] under the additional assumptions that $\\Omega$ is convex and $\\omega$ satisfies the condition $(\\alpha_1)$. In particular, our work solves Problem 9.7 in [1]."},"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":"1904.12836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-29T17:38:05Z","cross_cats_sorted":[],"title_canon_sha256":"e9e430446a70c7ada0b9e91ea6fcbd9d5663229dc672c0065e228d9c2e27a0be","abstract_canon_sha256":"999c0000c016c0ba87e06a502a31d1555d1c34128f812da5f499ca8d6b8f53c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:32.124456Z","signature_b64":"zU+JBDSqR5Zy4b/rF8r9O0dc+H4B4qXvUAf20SdqkvBC94xfwOkQcp1+MAH/FxJntrJ80RCl0ZBqi9mNbMuuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b3943a809f5a1cfbda0bed2eb3e23b8d44bdac255c4e3c7282affdb584f654b","last_reissued_at":"2026-05-17T23:47:32.123826Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:32.123826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A linear topological invariant for spaces of quasianalytic functions of Roumieu type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Debrouwere","submitted_at":"2019-04-29T17:38:05Z","abstract_excerpt":"We show that the spaces $\\mathcal{E}_{\\{\\omega\\}}(\\Omega)$ of ultradifferentiable functions of Roumieu type satisfy the dual interpolation estimate for small theta, where $\\omega$ is a quasianalytic weight function and $\\Omega$ is an arbitrary open subset of $\\mathbb{R}^d$. This result was previously shown by Bonet and Doma\\'nski [2] under the additional assumptions that $\\Omega$ is convex and $\\omega$ satisfies the condition $(\\alpha_1)$. In particular, our work solves Problem 9.7 in [1]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12836","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":"1904.12836","created_at":"2026-05-17T23:47:32.123941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.12836v1","created_at":"2026-05-17T23:47:32.123941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12836","created_at":"2026-05-17T23:47:32.123941+00:00"},{"alias_kind":"pith_short_12","alias_value":"TM4UHKAJ6WQ4","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"TM4UHKAJ6WQ47PNA","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"TM4UHKAJ","created_at":"2026-05-18T12:33:30.264802+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/TM4UHKAJ6WQ47PNAX3JOWPRDXD","json":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD.json","graph_json":"https://pith.science/api/pith-number/TM4UHKAJ6WQ47PNAX3JOWPRDXD/graph.json","events_json":"https://pith.science/api/pith-number/TM4UHKAJ6WQ47PNAX3JOWPRDXD/events.json","paper":"https://pith.science/paper/TM4UHKAJ"},"agent_actions":{"view_html":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD","download_json":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD.json","view_paper":"https://pith.science/paper/TM4UHKAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.12836&json=true","fetch_graph":"https://pith.science/api/pith-number/TM4UHKAJ6WQ47PNAX3JOWPRDXD/graph.json","fetch_events":"https://pith.science/api/pith-number/TM4UHKAJ6WQ47PNAX3JOWPRDXD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/action/storage_attestation","attest_author":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/action/author_attestation","sign_citation":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/action/citation_signature","submit_replication":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/action/replication_record"}},"created_at":"2026-05-17T23:47:32.123941+00:00","updated_at":"2026-05-17T23:47:32.123941+00:00"}