{"paper":{"title":"A linear topological invariant for spaces of quasianalytic functions of Roumieu type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Debrouwere","submitted_at":"2019-04-29T17:38:05Z","abstract_excerpt":"We show that the spaces $\\mathcal{E}_{\\{\\omega\\}}(\\Omega)$ of ultradifferentiable functions of Roumieu type satisfy the dual interpolation estimate for small theta, where $\\omega$ is a quasianalytic weight function and $\\Omega$ is an arbitrary open subset of $\\mathbb{R}^d$. This result was previously shown by Bonet and Doma\\'nski [2] under the additional assumptions that $\\Omega$ is convex and $\\omega$ satisfies the condition $(\\alpha_1)$. In particular, our work solves Problem 9.7 in [1]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12836","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"}