{"paper":{"title":"Heat kernels of non-symmetric L\\'evy-type operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Karol Szczypkowski, Tomasz Grzywny","submitted_at":"2018-04-04T09:21:25Z","abstract_excerpt":"We construct the fundamental solution (the heat kernel) $p^{\\kappa}$ to the equation $\\partial_t=\\mathcal{L}^{\\kappa}$, where under certain assumptions the operator $\\mathcal{L}^{\\kappa}$ takes one of the following forms, \\begin{align*} \\mathcal{L}^{\\kappa}f(x)&:= \\int_{\\mathbb{R}^d}( f(x+z)-f(x)- 1_{|z|<1} \\left<z,\\nabla f(x)\\right>)\\kappa(x,z)J(z)\\, dz \\,, \\mathcal{L}^{\\kappa}f(x)&:= \\int_{\\mathbb{R}^d}( f(x+z)-f(x))\\kappa(x,z)J(z)\\, dz\\,, \\mathcal{L}^{\\kappa}f(x)&:= \\frac1{2}\\int_{\\mathbb{R}^d}( f(x+z)+f(x-z)-2f(x))\\kappa(x,z)J(z)\\, dz\\,. \\end{align*} In particular, $J\\colon \\mathbb{R}^d \\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01313","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"}