{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:P43PHGOH64R3NS3HMDBDFSXLR2","short_pith_number":"pith:P43PHGOH","schema_version":"1.0","canonical_sha256":"7f36f399c7f723b6cb6760c232caeb8e8e333a35b37e373a72d0d19f693436f4","source":{"kind":"arxiv","id":"1807.03061","version":1},"attestation_state":"computed","paper":{"title":"On the norm-continuity for evolution family arising from non-autonomous forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"EL-Mennaoui Omar, Hafida Laasri","submitted_at":"2018-07-09T12:02:27Z","abstract_excerpt":"We consider evolution equations of the form \\begin{equation*}\\label{Abstract equation} \\dot u(t)+ A(t)u(t)=0,\\ \\ t\\in[0,T],\\ \\ u(0)=u_0, \\end{equation*} where $A(t),\\ t\\in [0,T],$ are associated with a non-autonomous sesquilinear form $\\mathfrak a(t,\\cdot,\\cdot)$ on a Hilbert space $H$ with constant domain $V\\subset H.$ In this note we continue the study of fundamental operator theoretical properties of the solutions. We give a sufficient condition for norm-continuity of evolution families on each spaces $V, H$ and on the dual space $V'$ of $V.$ The abstract results are applied to a class of e"},"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":"1807.03061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-09T12:02:27Z","cross_cats_sorted":[],"title_canon_sha256":"50108f5b93a758e7aae56c43870a9e5b56ed9d7e1e400a63cdbc620abe20e6ca","abstract_canon_sha256":"268f65a6d877fbe2ddf30df6f2dcd5862007606f5f273b3a42d7ce95e75ef853"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:12.998581Z","signature_b64":"i0TPnk1HgWKfryi1XmHyov2Zug1rw3q9cp5NdyBaLBfRgcX1Pci82MfiHqj13QJmybXLwZBfKNRpNxJr6OlMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f36f399c7f723b6cb6760c232caeb8e8e333a35b37e373a72d0d19f693436f4","last_reissued_at":"2026-05-18T00:11:12.997925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:12.997925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the norm-continuity for evolution family arising from non-autonomous forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"EL-Mennaoui Omar, Hafida Laasri","submitted_at":"2018-07-09T12:02:27Z","abstract_excerpt":"We consider evolution equations of the form \\begin{equation*}\\label{Abstract equation} \\dot u(t)+ A(t)u(t)=0,\\ \\ t\\in[0,T],\\ \\ u(0)=u_0, \\end{equation*} where $A(t),\\ t\\in [0,T],$ are associated with a non-autonomous sesquilinear form $\\mathfrak a(t,\\cdot,\\cdot)$ on a Hilbert space $H$ with constant domain $V\\subset H.$ In this note we continue the study of fundamental operator theoretical properties of the solutions. We give a sufficient condition for norm-continuity of evolution families on each spaces $V, H$ and on the dual space $V'$ of $V.$ The abstract results are applied to a class of e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03061","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":"1807.03061","created_at":"2026-05-18T00:11:12.998020+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.03061v1","created_at":"2026-05-18T00:11:12.998020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03061","created_at":"2026-05-18T00:11:12.998020+00:00"},{"alias_kind":"pith_short_12","alias_value":"P43PHGOH64R3","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"P43PHGOH64R3NS3H","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"P43PHGOH","created_at":"2026-05-18T12:32:43.782077+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/P43PHGOH64R3NS3HMDBDFSXLR2","json":"https://pith.science/pith/P43PHGOH64R3NS3HMDBDFSXLR2.json","graph_json":"https://pith.science/api/pith-number/P43PHGOH64R3NS3HMDBDFSXLR2/graph.json","events_json":"https://pith.science/api/pith-number/P43PHGOH64R3NS3HMDBDFSXLR2/events.json","paper":"https://pith.science/paper/P43PHGOH"},"agent_actions":{"view_html":"https://pith.science/pith/P43PHGOH64R3NS3HMDBDFSXLR2","download_json":"https://pith.science/pith/P43PHGOH64R3NS3HMDBDFSXLR2.json","view_paper":"https://pith.science/paper/P43PHGOH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.03061&json=true","fetch_graph":"https://pith.science/api/pith-number/P43PHGOH64R3NS3HMDBDFSXLR2/graph.json","fetch_events":"https://pith.science/api/pith-number/P43PHGOH64R3NS3HMDBDFSXLR2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P43PHGOH64R3NS3HMDBDFSXLR2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P43PHGOH64R3NS3HMDBDFSXLR2/action/storage_attestation","attest_author":"https://pith.science/pith/P43PHGOH64R3NS3HMDBDFSXLR2/action/author_attestation","sign_citation":"https://pith.science/pith/P43PHGOH64R3NS3HMDBDFSXLR2/action/citation_signature","submit_replication":"https://pith.science/pith/P43PHGOH64R3NS3HMDBDFSXLR2/action/replication_record"}},"created_at":"2026-05-18T00:11:12.998020+00:00","updated_at":"2026-05-18T00:11:12.998020+00:00"}