{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KWR6JAMRIYOPAV53FV6FD4HK4Z","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":"9d25008598b350e4dc3abea0c72b34825f2f2ab8fd45c17d337c20a07d70ed59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-11-05T17:48:03Z","title_canon_sha256":"1d0e468d1c341ea26554144e126020e01f1e3ac71ef00506304e4018dfa30007"},"schema_version":"1.0","source":{"id":"1811.01876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01876","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01876v1","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01876","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"KWR6JAMRIYOP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KWR6JAMRIYOPAV53","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KWR6JAMR","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:ea6f647d7919984c148cfb6d604c2e72a871122eb484cf980f4af7348a39b697","target":"graph","created_at":"2026-05-18T00:01:33Z","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":"Let $(T(t))_{t\\geq 0}$ be a $C_0$ semigroup on a Banach space $X$ with infinitesimal generator $A$. In this work, we give conditions for which the spectral mapping theorem $\\sigma_{*}(T(t))\\backslash \\{0\\}=\\{e^{\\lambda s}, \\lambda\\in\\sigma_{*}(A)\\}$ holds, where $\\sigma_*$ can be equal to the essential, Browder and Kato spectrum. Also, we will be interested in the relations between the spectrum of $A$ and the spectrum of the nth derivative $T(t)^{(n)}$ of a differentiable $C_0$ semigroup $(T(t))_{t\\geq0}$.","authors_text":"Abdelaziz Tajmouati, Hamid Boua, Mohammed Karmouni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-11-05T17:48:03Z","title":"Spectral mapping theorems of differentiable C0 semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01876","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:c5f2ff7d2e4cbb86ba6ed34e879cff0803226932e75cc5a6993c10a426e289aa","target":"record","created_at":"2026-05-18T00:01:33Z","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":"9d25008598b350e4dc3abea0c72b34825f2f2ab8fd45c17d337c20a07d70ed59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-11-05T17:48:03Z","title_canon_sha256":"1d0e468d1c341ea26554144e126020e01f1e3ac71ef00506304e4018dfa30007"},"schema_version":"1.0","source":{"id":"1811.01876","kind":"arxiv","version":1}},"canonical_sha256":"55a3e48191461cf057bb2d7c51f0eae642ba10310da7fe04a51ba76e09883683","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55a3e48191461cf057bb2d7c51f0eae642ba10310da7fe04a51ba76e09883683","first_computed_at":"2026-05-18T00:01:33.021554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:33.021554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V2kGXC/xXMSiwxKE76EAfmm5OvwE317J6tsL0wRlPQcrgPbdia63czFM8nU4UBkWoC+5Lu2KP+D1/NyaD2JcCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:33.022134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01876","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5f2ff7d2e4cbb86ba6ed34e879cff0803226932e75cc5a6993c10a426e289aa","sha256:ea6f647d7919984c148cfb6d604c2e72a871122eb484cf980f4af7348a39b697"],"state_sha256":"a1a7f3352bd44b968ea4b34bbd91358416fed42f5dd0d648b54db79fd453b25d"}