{"paper":{"title":"Two-sided optimal bounds for Green function of half-spaces for relativistic $\\alpha$-stable process","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Micha{\\l} Ryznar, Tomasz Grzywny","submitted_at":"2007-06-08T12:47:12Z","abstract_excerpt":"The purpose of this paper is to find optimal estimates for the Green function of a half-space of {\\it the relativistic $\\alpha$-stable process} with parameter $m$ on $\\Rd$ space. This process has an infinitesimal generator of the form $mI-(m^{2/\\alpha}I-\\Delta)^{\\alpha/2},$ where $0<\\alpha<2$, $m>0$, and reduces to the isotropic $\\alpha$-stable process for $m=0$. Its potential theory for open bounded sets has been well developed throughout the recent years however almost nothing was known about the behaviour of the process on unbounded sets. The present paper is intended to fill this gap and w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1175","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"}