{"paper":{"title":"Functions of unitaries with $\\mathcal{S}^p$-perturbations for non continuously differentiable functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cl\\'ement Coine","submitted_at":"2024-06-19T08:34:10Z","abstract_excerpt":"Consider a function $f : \\mathbb{T} \\to \\mathbb{C}$, $n$-times differentiable on $\\mathbb{T}$ and such that its $n$th derivative $f^{(n)}$ is bounded but not necessarily continuous. Let $U : \\mathbb{R} \\to \\mathcal{U}(\\mathcal{H})$ be a function taking values in the set of unitary operators on some separable Hilbert space $\\mathcal{H}$. Let $1<p<\\infty$ and let $\\mathcal{S}^p(\\mathcal{H})$ be the Schatten class of order $p$ on $\\mathcal{H}$. If $\\tilde{U}:t\\in\\mathbb{R} \\mapsto U(t)-U(0)$ is $n$-times $\\mathcal{S}^p$-differentiable on $\\mathbb{R}$, we show that the operator valued function $\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.13333","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.13333/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"}