{"paper":{"title":"Holomorphic families of forms, operators and $C_0$-semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Hendrik Vogt, J\\\"urgen Voigt","submitted_at":"2017-07-04T11:36:00Z","abstract_excerpt":"If $z\\mapsto a_z$ is a holomorphic function with values in the sectorial forms in a Hilbert space, then the associated operator valued function $z\\mapsto A_z$ is resolvent holomorphic. We give a proof of this result of Kato, on the basis of the Lax-Milgram lemma. We also show that the $C_0$-semigroups $T_z$ generated by $-A_z$ depend holomorphically on $z$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00923","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"}