{"paper":{"title":"Intrinsic Contractivity of Feynman-Kac Semigroups for Symmetric Jump Processes with Infinite Range Jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Xin Chen","submitted_at":"2015-01-25T08:28:27Z","abstract_excerpt":"Let $(X_t)_{t\\ge 0}$ be a symmetric strong Markov process generated by non-local regular Dirichlet form $(D,\\D(D))$ as follows \\begin{equation*} \\begin{split} & D(f,g)=\\int_{\\R^d}\\int_{\\R^d}\\big(f(x)-f(y)\\big)\\big(g(x)-g(y)\\big) J(x,y)\\,dx\\,dy, \\quad f,g\\in \\D(D) \\end{split} \\end{equation*} where $J(x,y)$ is a strictly positive and symmetric measurable function on $\\R^d\\times \\R^d$. We study the intrinsic hypercontractivity, intrinsic supercontractivity and intrinsic ultracontractivity for the Feynman-Kac semigroup $$ T^V_t(f)(x)=\\Ee^x\\left(\\exp\\Big(-\\int_0^tV(X_s)\\,ds\\Big)f(X_t)\\right),\\,\\, x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06128","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"}