{"paper":{"title":"Intrinsic Ultracontractivity of Feynman-Kac Semigroups for Symmetric Jump Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Xin Chen","submitted_at":"2014-03-14T05:26:26Z","abstract_excerpt":"Consider the symmetric non-local Dirichlet form $(D,\\D(D))$ given by $$ D(f,f)=\\int_{\\R^d}\\int_{\\R^d}\\big(f(x)-f(y)\\big)^2 J(x,y)\\,dx\\,dy $$with $\\D(D)$ the closure of the set of $C^1$ functions on $\\R^d$ with compact support under the norm $\\sqrt{D_1(f,f)}$, where $D_1(f,f):=D(f,f)+\\int f^2(x)\\,dx$ and $J(x,y)$ is a nonnegative symmetric measurable function on $\\R^d\\times \\R^d$. Suppose that there is a Hunt process $(X_t)_{t\\ge 0}$ on $\\R^d$ corresponding to $(D,\\D(D))$, and that $(L,\\D(L))$ is its infinitesimal generator. We study the intrinsic ultracontractivity for the Feynman-Kac semigrou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3486","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"}