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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","authors_text":"Jing Zhang, Wei Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-14T19:00:57Z","title":"Levy-Khintchine type representation of Dirichlet generators and Semi-Dirichlet forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3552","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a241951e86874ebc021b7f944d19c4e10ccbb9e8e8c6bca2133ee82e7516c069","target":"record","created_at":"2026-05-18T03:28:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"988f09b24857098151c23465facd71cecf7ec405f3c92db3bfce2e73701d71f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-14T19:00:57Z","title_canon_sha256":"86bb64de5c71a9575ad96f6e48e2def05390e3f2940a1f543dc14b7e2cdea59c"},"schema_version":"1.0","source":{"id":"1303.3552","kind":"arxiv","version":2}},"canonical_sha256":"d4db9fb1fbc6973d1f2be966ecfe792462264546ecbeca0007c154ba7a2d2720","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4db9fb1fbc6973d1f2be966ecfe792462264546ecbeca0007c154ba7a2d2720","first_computed_at":"2026-05-18T03:28:16.955699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:16.955699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OBYcyl8QXx6B9v3bEkSdnQkFTefPrJtp/JbI0GyqlP2rdmupc16h0rKLjixu5L0iVse5yaHTRTtF+LKG5VinCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:16.956430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3552","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a241951e86874ebc021b7f944d19c4e10ccbb9e8e8c6bca2133ee82e7516c069","sha256:37ed9a264c773cd1f6d17cd0f9995e3d993ce2536d7458871894d3ba05403021"],"state_sha256":"cb7ac5c733576340d4227c7353398587ad6a4b6b08d10f611653f27aa5994dad"}