{"paper":{"title":"Admissible operators and ${\\mathcal H}_{\\infty}$ calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hans Zwart","submitted_at":"2010-01-20T07:36:25Z","abstract_excerpt":"Given a Hilbert space and the generator $A$ of a strongly continuous, exponentially stable, semigroup on this Hilbert space. For any $g(-s) \\in {\\mathcal H}_{\\infty}$ we show that there exists an infinite-time admissible output operator $g(A)$. If $g$ is rational, then this operator is bounded, and equals the \"normal\" definition of $g(A)$. In particular, when $g(s)=1/(s + \\alpha)$, $ \\alpha \\in {\\mathbb C}_0^+$, then this admissible output operator equals $(\\alpha I - A)^{-1}$. Although in general $g(A)$ may be unbounded, we always have that $g(A)$ multiplied by the semigroup is a bounded oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3482","kind":"arxiv","version":2},"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"}