{"paper":{"title":"Levy-Khintchine type representation of Dirichlet generators and Semi-Dirichlet forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jing Zhang, Wei Sun","submitted_at":"2013-03-14T19:00:57Z","abstract_excerpt":"Let $U$ be an open set of $\\mathbb{R}^n$, $m$ a positive Radon measure on $U$ such that ${\\rm supp}[m]=U$, and $(P_t)_{t>0}$ a strongly continuous contraction sub-Markovian semigroup on $L^2(U;m)$. We investigate the structure of $(P_t)_{t>0}$.\n  (i) Denote respectively by $(A,D(A))$ and $(\\hat A,D(\\hat A))$ the generator and the co-generator of $(P_t)_{t>0}$. Under the assumption that $C^{\\infty}_0(U)\\subset D(A)\\cap D(\\hat A)$, we give an explicit L\\'evy-Khintchine type representation of $A$ on $C^{\\infty}_0(U)$.\n  (ii) If $(P_t)_{t>0}$ is an analytic semigroup and hence is associated with a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3552","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"}