{"paper":{"title":"On the First Eigenfunction of the Symmetric Stable Process in a Bounded Lipschitz Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.PR","authors_text":"Dante DeBlassie, Rodrigo Banuelos","submitted_at":"2013-10-29T16:39:51Z","abstract_excerpt":"We give a proof that the first eigenfunction of the $\\alpha$-symmetric stable process on a bounded Lipschitz domain in $\\R^d$, $d\\geq 1$, is superharmonic for $\\alpha=2/m$, where $m>2$ is an integer. This result was first proved for the ball by M. Ka{\\ss}mann and L. Silvestre (personal communication) with different methods. For $\\alpha=1$, the result was proved in \\cite[Theorem 4.7]{BanKul}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7869","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"}