{"paper":{"title":"Standard subspaces of Hilbert spaces of holomorphic functions on tube domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Bent {\\O}rsted, Gestur Olafsson, Karl-Hermann Neeb","submitted_at":"2020-07-29T12:43:19Z","abstract_excerpt":"In this article we study standard subspaces of Hilbert spaces of vector-valued holomorphic functions on tube domains E + i C^0, where C \\subeq E is a pointed generating cone invariant under e^{R h} for some endomorphism h \\in \\End(E), diagonalizable with the eigenvalues 1,0,-1 (generalizing a Lorentz boost). This data specifies a wedge domain W(E,C,h) \\subeq E and one of our main results exhibits corresponding standard subspaces as being generated using test functions on these domains. We also investigate aspects of reflection positivity for the triple (E,C,e^{\\pi i h}) and the support propert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.14797","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.14797/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}