{"paper":{"title":"Estimates for the Poisson kernel and the evolution kernel on nilpotent meta-abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.FA","authors_text":"Richard Penney, Roman Urban","submitted_at":"2011-08-11T20:40:24Z","abstract_excerpt":"Let $S$ be a semi direct product $S=N\\rtimes A$ where $N$ is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and $A$ is isomorphic with $\\R^k,$ $k>1.$ We consider a class of second order left-invariant differential operators on $S$ of the form $\\mathcal L_\\alpha=L^a+\\Delta_\\alpha,$ where $\\alpha\\in\\R^k,$ and for each $a\\in\\R^k,$ $L^a$ is left-invariant second order differential operator on $N$ and $\\Delta_\\alpha=\\Delta-<\\alpha,\\nabla>,$ where $\\Delta$ is the usual Laplacian on $\\R^k.$ Using some probabilistic techniques (e.g., skew-product formulas for diffusion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2515","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"}