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In both cases, the time dependent operators $A(t)$ are associated with a family of sesquilinear forms and the multiplicative left or right perturbations $B(t)$ as well as the additive perturbation $P(t)$ are families of bounded operators on the considered Hilbert space. We prove maximal $L_p$-regularity results and other regularity properties for the solutions of the previous problems under minimal regul"},"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":"1607.00254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-01T14:13:37Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a1ffebf01afe98518ace29c0a58c792d02fbd0d1d1596f1d601556b7811b9856","abstract_canon_sha256":"1edb76fd784da52023be0458ab83deeb9224dcf6c46b757d9b172eb24f85411f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:28.519861Z","signature_b64":"fw+Cdz7IkLUPOM895nWPMFb0pvw1OLhN54ADqH+ewiUEW7Ce9XyTeSFLoTW37uGMXNyN29zxT36+E81MgEjPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9410fb124f91e0d0da50839e46ec94536242a688f57c3ff3cb32b94687d53e0f","last_reissued_at":"2026-05-18T01:08:28.519425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:28.519425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-autonomous right and left multiplicative perturbations and maximal regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"El Maati Ouhabaz (UB, IMB), Mahdi Achache (IMB)","submitted_at":"2016-07-01T14:13:37Z","abstract_excerpt":"We consider the problem of maximal regularity for non-autonomous Cauchy problems $u'(t) + B(t)A(t)u(t) + P(t)u(t) = f(t), u(0) = u_0$ and $u'(t) + A(t)B(t)u(t) + P(t)u(t) = f (t), u(0) = u_0$. In both cases, the time dependent operators $A(t)$ are associated with a family of sesquilinear forms and the multiplicative left or right perturbations $B(t)$ as well as the additive perturbation $P(t)$ are families of bounded operators on the considered Hilbert space. We prove maximal $L_p$-regularity results and other regularity properties for the solutions of the previous problems under minimal regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00254","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":"1607.00254","created_at":"2026-05-18T01:08:28.519492+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.00254v1","created_at":"2026-05-18T01:08:28.519492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00254","created_at":"2026-05-18T01:08:28.519492+00:00"},{"alias_kind":"pith_short_12","alias_value":"SQIPWESPSHQN","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SQIPWESPSHQNBWSQ","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SQIPWESP","created_at":"2026-05-18T12:30:44.179134+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/SQIPWESPSHQNBWSQQOPEN3EUKN","json":"https://pith.science/pith/SQIPWESPSHQNBWSQQOPEN3EUKN.json","graph_json":"https://pith.science/api/pith-number/SQIPWESPSHQNBWSQQOPEN3EUKN/graph.json","events_json":"https://pith.science/api/pith-number/SQIPWESPSHQNBWSQQOPEN3EUKN/events.json","paper":"https://pith.science/paper/SQIPWESP"},"agent_actions":{"view_html":"https://pith.science/pith/SQIPWESPSHQNBWSQQOPEN3EUKN","download_json":"https://pith.science/pith/SQIPWESPSHQNBWSQQOPEN3EUKN.json","view_paper":"https://pith.science/paper/SQIPWESP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.00254&json=true","fetch_graph":"https://pith.science/api/pith-number/SQIPWESPSHQNBWSQQOPEN3EUKN/graph.json","fetch_events":"https://pith.science/api/pith-number/SQIPWESPSHQNBWSQQOPEN3EUKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SQIPWESPSHQNBWSQQOPEN3EUKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SQIPWESPSHQNBWSQQOPEN3EUKN/action/storage_attestation","attest_author":"https://pith.science/pith/SQIPWESPSHQNBWSQQOPEN3EUKN/action/author_attestation","sign_citation":"https://pith.science/pith/SQIPWESPSHQNBWSQQOPEN3EUKN/action/citation_signature","submit_replication":"https://pith.science/pith/SQIPWESPSHQNBWSQQOPEN3EUKN/action/replication_record"}},"created_at":"2026-05-18T01:08:28.519492+00:00","updated_at":"2026-05-18T01:08:28.519492+00:00"}