{"paper":{"title":"On Properties of Geometric Preduals of ${\\mathbf C^{k,\\omega}}$ Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander Brudnyi","submitted_at":"2016-07-17T03:27:56Z","abstract_excerpt":"Let $C_b^{k,\\omega}(\\mathbb R^n)$ be the Banach space of $C^k$ functions on $\\mathbb R^n$ bounded together with all derivatives of order $\\le k$ and with derivatives of order $k$ having moduli of continuity majorated by $c\\cdot\\omega$, $c\\in\\mathbb R_+$, for some $\\omega\\in C(\\mathbb R_+)$. Let $C_b^{k,\\omega}(S):=C_b^{k,\\omega}(\\mathbb R^n)|_S$ be the trace space to a closed subset $S\\subset\\mathbb R^n$. The geometric predual $G_b^{k,\\omega}(S)$ of $C_b^{k,\\omega}(S)$ is the minimal closed subspace of the dual $\\bigl(C_b^{k,\\omega}(\\mathbb R^n)\\bigr)^*$ containing evaluation functionals of po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04824","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"}