{"paper":{"title":"Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Dachun Yang, Eero Saksman, Feng Dai, Wen Yuan, Yangyang Zhang","submitted_at":"2025-08-29T00:04:24Z","abstract_excerpt":"Let $\\Lambda_s$ denote the inhomogeneous Lipschitz space of order $s\\in(0,\\infty)$ on $\\mathbb{R}^n$. This article characterizes the distance $d(f, V)_{\\Lambda_s}: = \\inf_{g\\in V} \\|f-g\\|_{\\Lambda_s}$ from a function $f\\in \\Lambda_s$ to a non-dense subspace $V\\subset \\Lambda_s$ via the fractional semigroup $\\{T_{\\alpha, t}: =e^{-t (-\\Delta)^{\\alpha/2}}: t\\in (0, \\infty)\\}$ for any $\\alpha\\in(0,\\infty)$. Given an integer $ r >s/\\alpha$, a uniformly bounded continuous function $f$ on $\\mathbb{R}^n$ belongs to the space $\\Lambda_s$ if and only if there exists a constant $\\lambda\\in(0,\\infty)$ suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.21269","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/2508.21269/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"}