{"paper":{"title":"Trotter product formula and linear evolution equations on Hilbert spaces On the occasion of the 100th birthday of Tosio Kato","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Artur Stephan, Hagen Neidhardt, Valentin Zagrebnov (I2M)","submitted_at":"2019-01-08T08:39:54Z","abstract_excerpt":"The paper is devoted to evolution equations of the form $\\partial$ $\\partial$t u(t) = --(A + B(t))u(t), t $\\in$ I = [0, T ], on separable Hilbert spaces where A is a non-negative self-adjoint operator and B($\\times$) is family of non-negative self-adjoint operators such that dom(A $\\alpha$) $\\subseteq$ dom(B(t)) for some $\\alpha$ $\\in$ [0, 1) and the map A --$\\alpha$ B($\\times$)A --$\\alpha$ is H{\\\"o}lder continuous with the H{\\\"o}lder exponent $\\beta$ $\\in$ (0, 1). It is shown that the solution operator U(t, s) of the evolution equation can be approximated in the operator norm by a combination"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02205","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"}