{"paper":{"title":"On subordination of holomorphic semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.FA","authors_text":"Alexander Gomilko, Yuri Tomilov","submitted_at":"2014-08-06T20:42:16Z","abstract_excerpt":"We prove that for any Bernstein function $\\psi$ the operator $-\\psi(A)$ generates a holomorphic $C_0$-semigroup $(e^{-t\\psi(A)})_{t \\ge 0}$ on a Banach space, whenever $-A$ does. This answers a question posed by Kishimoto and Robinson. Moreover, giving a positive answer to a question by Berg, Boyadzhiev and de Laubenfels,  we show that $(e^{-t\\psi(A)})_{t \\ge 0}$ is holomorphic in the holomorphy sector of $(e^{-tA})_{t \\ge 0},$ and if $(e^{-tA})_{t \\ge 0}$ is sectorially bounded in this sector then $(e^{-t\\psi(A)})_{t \\ge 0}$ has the same property. We also obtain new sufficient conditions on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1417","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"}