{"paper":{"title":"Amenability and harmonic $L^p$-functions on hypergroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jila Sohaei, Mehdi Nemati","submitted_at":"2019-06-12T13:14:22Z","abstract_excerpt":"Let $K$ be a locally compact hypergroup with a left invariant Haar measure. We show that the Liouville property and amenability are equivalent for $K$ when it is second countable. Suppose that $\\sigma$ is a non-degenerate probability measure on $K$, we show that there is no non-trivial $\\sigma$-harmonic function which is continuous and vanishing at infinity. Using this, we prove that the space $H_\\sigma^p(K)$ of all $\\sigma$-harmonic $L^p$-functions, is trivial for all $1\\leq p<\\infty$. Further, it is shown that $H_\\sigma^\\infty(K)$ contains only constant functions if and only if it is a subal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05124","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"}