{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SY25YPQRULIOTX6XOSXSWLKUZF","short_pith_number":"pith:SY25YPQR","schema_version":"1.0","canonical_sha256":"9635dc3e11a2d0e9dfd774af2b2d54c958d084b95ea52cd3ca3c51a924bfe410","source":{"kind":"arxiv","id":"1407.7603","version":1},"attestation_state":"computed","paper":{"title":"On some smoothening effects of the transition semigroup of a L\\'evy process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lihu Xu, Szymon Peszat, Zhao Dong","submitted_at":"2014-07-28T23:58:20Z","abstract_excerpt":"Let $(P_t)$ be the transition semigroup of a L\\'evy process $L$ taking values in a Hilbert space $H$. Let $\\nu$ be the L\\'evy measure of $L$. It is shown that for any bounded and measurable function $f$, $$ \\int_H\\left\\vert P_tf(x+y)-P_tf(x)\\right\\vert ^2 \\nu (\\dif y)\\le \\frac 1 t P_tf^2(x) \\qquad \\text{for all $t>0$, $x\\in H$.} $$ As $\\nu$ can be infinite this formula establishes some smoothening effect of the semigroup $(P_t)$. In the paper some applications of the formula will be presented as well."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.7603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-28T23:58:20Z","cross_cats_sorted":[],"title_canon_sha256":"67e6f71ed76001f39a5f2dac3285a51075ceb112d39d049cc0413c08f4b597d1","abstract_canon_sha256":"98477448df76e216f62d0064587f4b901c59d2e7459e66c92ca713def9419fb8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:22.239018Z","signature_b64":"NzbIhTyHPdi+2D4igNya7xspOYqVbmpWrbxf6ewVZy4YtxZHFx6MWT+mx247j0VrryZwMRipvQzAqAUC+JKoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9635dc3e11a2d0e9dfd774af2b2d54c958d084b95ea52cd3ca3c51a924bfe410","last_reissued_at":"2026-05-18T02:46:22.238549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:22.238549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some smoothening effects of the transition semigroup of a L\\'evy process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lihu Xu, Szymon Peszat, Zhao Dong","submitted_at":"2014-07-28T23:58:20Z","abstract_excerpt":"Let $(P_t)$ be the transition semigroup of a L\\'evy process $L$ taking values in a Hilbert space $H$. Let $\\nu$ be the L\\'evy measure of $L$. It is shown that for any bounded and measurable function $f$, $$ \\int_H\\left\\vert P_tf(x+y)-P_tf(x)\\right\\vert ^2 \\nu (\\dif y)\\le \\frac 1 t P_tf^2(x) \\qquad \\text{for all $t>0$, $x\\in H$.} $$ As $\\nu$ can be infinite this formula establishes some smoothening effect of the semigroup $(P_t)$. In the paper some applications of the formula will be presented as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7603","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.7603","created_at":"2026-05-18T02:46:22.238621+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.7603v1","created_at":"2026-05-18T02:46:22.238621+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7603","created_at":"2026-05-18T02:46:22.238621+00:00"},{"alias_kind":"pith_short_12","alias_value":"SY25YPQRULIO","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SY25YPQRULIOTX6X","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SY25YPQR","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF","json":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF.json","graph_json":"https://pith.science/api/pith-number/SY25YPQRULIOTX6XOSXSWLKUZF/graph.json","events_json":"https://pith.science/api/pith-number/SY25YPQRULIOTX6XOSXSWLKUZF/events.json","paper":"https://pith.science/paper/SY25YPQR"},"agent_actions":{"view_html":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF","download_json":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF.json","view_paper":"https://pith.science/paper/SY25YPQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.7603&json=true","fetch_graph":"https://pith.science/api/pith-number/SY25YPQRULIOTX6XOSXSWLKUZF/graph.json","fetch_events":"https://pith.science/api/pith-number/SY25YPQRULIOTX6XOSXSWLKUZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF/action/storage_attestation","attest_author":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF/action/author_attestation","sign_citation":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF/action/citation_signature","submit_replication":"https://pith.science/pith/SY25YPQRULIOTX6XOSXSWLKUZF/action/replication_record"}},"created_at":"2026-05-18T02:46:22.238621+00:00","updated_at":"2026-05-18T02:46:22.238621+00:00"}