{"paper":{"title":"Spectral condition, hitting times and Nash inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dasha Loukianova, Eva Loecherbach, Oleg Loukianov","submitted_at":"2011-03-23T20:30:43Z","abstract_excerpt":"Let $X$ be a $\\mu$-symmetric Hunt process on a LCCB space E. For an open set G $\\subseteq$ E, let $\\tau_G$ be the exit time of $X$ from G and $A^G$ be the generator of the process killed when it leaves G. Let $r:[0,\\infty[\\to[0,\\infty[$ and $R (t) = \\int_0^t r(s) ds$.\n  We give necessary and sufficient conditions for $\\E_{\\mu} R (\\tau_G)<\\infty$ in terms of the behavior near the origin of the spectral measure of $-A^G.$\n  When $r(t)=t^l$, $l>0$, by means of this condition we derive the Nash inequality for the killed process.\n  In the case of one-dimensional diffusions, this permits to show tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4622","kind":"arxiv","version":3},"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"}