{"paper":{"title":"Boundary values of resolvents of self-adjoint operators in Krein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Christian G\\'erard (LM-Orsay), Dietrich H\\\"afner (IF), Vladimir Georgescu (AGM)","submitted_at":"2012-11-05T08:50:34Z","abstract_excerpt":"We prove in this paper resolvent estimates for the boundary values of resolvents of selfadjoint operators on a Krein space: if $H$ is a selfadjoint operator on a Krein space $\\cH$, equipped with the Krein scalar product $\\langle \\cdot| \\cdot \\rangle$, $A$ is the generator of a $C_{0}-$group on $\\cH$ and $I\\subset \\rr$ is an interval such that: \\begin{itemize} \\item[]1) $H$ admits a Borel functional calculus on $I$, \\item[]2) the spectral projection $\\one_{I}(H)$ is positive in the Krein sense, \\item[]3) the following {\\em positive commutator estimate} holds: \\[ \\Re \\langle u| [H, \\i A]u\\rangle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0791","kind":"arxiv","version":4},"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"}