{"paper":{"title":"Compactness and Density Estimates for Weighted Fractional Heat Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang","submitted_at":"2018-05-10T18:55:26Z","abstract_excerpt":"We prove that the operator $L_0=-(1+|x|)^\\beta(-\\Delta)^{\\alpha/2}$ with $\\alpha\\in(0,2)$, $d>\\alpha$ and $\\beta\\ge0$ generates a compact semigroup or resolvent on $L^2(\\R^d;(1+|x|)^{-\\beta}\\,dx)$, if and only if $\\beta>\\alpha$. When $\\beta>\\alpha$, we obtain two-sided asymptotic estimates for high order eigenvalues, and sharp bounds for the corresponding heat kernel."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04135","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"}