{"paper":{"title":"Spatial asymptotics at infinity for heat kernels of integro-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.AP","authors_text":"Kamil Kaleta, Pawe{\\l} Sztonyk","submitted_at":"2017-05-31T08:57:37Z","abstract_excerpt":"We study a spatial asymptotic behaviour at infinity of kernels $p_t(x)$ for convolution semigroups of nonlocal pseudo-differential operators. We give general and sharp sufficient conditions under which the limits $$\n  \\lim_{r \\to \\infty} \\frac{p_t(r\\theta-y)}{t \\, \\nu(r\\theta)}, \\quad t \\in T, \\ \\ \\theta \\in E, \\ \\ y \\in \\mathbb R^d, $$ exist and can be effectively computed. Here $\\nu$ is the corresponding L\\'evy density, $T \\subset (0,\\infty)$ is a bounded time-set and $E$ is a subset of the unit sphere in $\\mathbb R^d$, $d \\geq 1$. Our results are local on the unit sphere. They apply to a wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10992","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"}