{"paper":{"title":"Heat Kernel for Fractional Diffusion Operators with Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Feng-Yu Wang, Xicheng Zhang","submitted_at":"2012-04-23T01:20:37Z","abstract_excerpt":"Let $L$ be an elliptic differential operator on a complete connected Riemannian manifold $M$ such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussian type gradient estimate. Let $L^{(\\aa)}$ be the $\\aa$-stable subordination of $L$ for $\\aa\\in (1,2).$ We found some classes $\\mathbb K_\\aa^{\\gg,\\bb} (\\bb,\\gg\\in [0,\\aa))$ of time-space functions containing the Kato class, such that for any measurable $b: [0,\\infty)\\times M\\to TM$ and $c: [0,\\infty)\\times M\\to M$ with $|b|, c\\in \\mathbb K_\\aa^{1,1},$ the operator $$L_{b,c}^{(\\aa)}(t,x):= L^{(\\aa)}(x)+  <b(t,x),\\nn \\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4956","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"}