{"paper":{"title":"Heavy tailed approximate identities and $\\sigma$-stable Markov kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Federico Morana, Hugo Aimar, Ivana G\\'omez","submitted_at":"2017-01-11T21:07:13Z","abstract_excerpt":"The aim of this paper is to present some results relating the properties of stability, concentration and approximation to the identity of convolution through not necessarily mollification type families of heavy tailed Markov kernels. A particular case is provided by the kernels $K_t$ obtained as the $t$ mollification of $L^{\\sigma(t)}$ selected from the family $\\mathcal{L}=\\{L^{\\sigma}: \\widehat{L^{\\sigma}}(\\xi)=e^{-|\\xi|^\\sigma},0<\\sigma<2\\}$, by a given function $\\sigma$ with values in the interval $(0,2)$. We show that a basic Harnack type inequality, introduced by C.~Calder\\'{o}n in the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03170","kind":"arxiv","version":2},"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"}