{"paper":{"title":"Unavoidable collections of balls for processes with isotropic unimodal Green function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Wolfhard Hansen","submitted_at":"2014-03-01T11:41:18Z","abstract_excerpt":"Let us suppose that we have a right continuous Markov semigroup on $R^d$, $d\\ge 1$, such that its potential kernel is given by convolution with a function $G_0=g(|\\cdot|)$, where $g$ is decreasing, has a mild lower decay property at zero, and a very weak decay property at infinity. This captures not only the Brownian semigroup (classical potential theory) and isotropic $\\alpha$-stable semigroups (Riesz potentials), but also more general isotropic L\\'evy processes, where the characteristic function has a certain lower scaling property, and various geometric stable processes.\n  There always exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0076","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"}