{"paper":{"title":"Optimal kernel estimates for a Schr\\\"odinger type operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Canale, Cristian Tacelli","submitted_at":"2016-04-13T20:12:13Z","abstract_excerpt":"In the paper the principal result obtained is the estimate for the heat kernel associated to the Schr\\\"odinger type operator $(1+|x|^\\alpha)\\Delta-|x|^\\beta$ \\[ k(t,x,y)\\leq Ct^{-\\frac{\\theta}{2}}\\frac {\\varphi(x)\\varphi(y)}{1+|x|^\\alpha}, \\] where $\\varphi=(1+|x|^\\alpha)^{\\frac{2-\\theta}{4}+\\frac{1}{\\alpha}\\frac{\\theta-N}{2}}$, $\\theta\\geq N$ and $0<t<1$, provided that $N>2$, $\\alpha> 2$ and $\\beta>\\alpha-2$. This estimate improves a similar estimate in \\cite {can-rhan-tac2} with respect to the dependence on spatial component."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03960","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"}