{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZSITOWRQEYVZI3B6V6OOEZRI4L","short_pith_number":"pith:ZSITOWRQ","schema_version":"1.0","canonical_sha256":"cc91375a30262b946c3eaf9ce26628e2e63c00038961bebee3e63be45234602f","source":{"kind":"arxiv","id":"1503.02895","version":2},"attestation_state":"computed","paper":{"title":"Form Inequalities for Symmetric Contraction Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.SP"],"primary_cat":"math.FA","authors_text":"Markus Haase","submitted_at":"2015-03-10T13:17:35Z","abstract_excerpt":"Consider --- for the generator \\({-}A\\) of a symmetric contraction semigroup over some measure space $\\mathrm{X}$, $1\\le p < \\infty$, $q$ the dual exponent and given measurable functions $F_j,\\: G_j : \\mathbb{C}^d \\to \\mathbb{C}$ --- the statement: $$ \\mathrm{Re}\\, \\sum_{j=1}^m \\int_{\\mathrm{X}} A F_j(\\mathbf{f}) \\cdot G_j(\\mathbf{f}) \\,\\,\\ge \\,\\,0 $$ {\\em for all $\\mathbb{C}^d$-valued measurable functions $\\mathbf{f}$ on $\\mathrm{X}$ such that $F_j(\\mathbf{f}) \\in \\mathrm{dom}(A_p)$ and $G_j(\\mathbf{f}) \\in \\mathrm{L}^q(\\mathrm{X})$ for all $j$.}\n  It is shown that this statement is valid in "},"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":"1503.02895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-10T13:17:35Z","cross_cats_sorted":["math.PR","math.SP"],"title_canon_sha256":"5f31c60162f5c5a9637196dd6f28fdbd5688ff32c099a021e5a335f6aec033de","abstract_canon_sha256":"a8c8da89bfd25c5de097311cf8bfc6df2ca37d5fedf801fc681556364d12ec1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:34.992917Z","signature_b64":"mHHrTKrCvfutQ/GR8VR0YuV4YLTkExDLgOYhCqhAPFZcdKRVHnylgVQSUNbaHwZl2plCIiH0xfHIZF8lTPe4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc91375a30262b946c3eaf9ce26628e2e63c00038961bebee3e63be45234602f","last_reissued_at":"2026-05-18T01:34:34.992221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:34.992221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Form Inequalities for Symmetric Contraction Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.SP"],"primary_cat":"math.FA","authors_text":"Markus Haase","submitted_at":"2015-03-10T13:17:35Z","abstract_excerpt":"Consider --- for the generator \\({-}A\\) of a symmetric contraction semigroup over some measure space $\\mathrm{X}$, $1\\le p < \\infty$, $q$ the dual exponent and given measurable functions $F_j,\\: G_j : \\mathbb{C}^d \\to \\mathbb{C}$ --- the statement: $$ \\mathrm{Re}\\, \\sum_{j=1}^m \\int_{\\mathrm{X}} A F_j(\\mathbf{f}) \\cdot G_j(\\mathbf{f}) \\,\\,\\ge \\,\\,0 $$ {\\em for all $\\mathbb{C}^d$-valued measurable functions $\\mathbf{f}$ on $\\mathrm{X}$ such that $F_j(\\mathbf{f}) \\in \\mathrm{dom}(A_p)$ and $G_j(\\mathbf{f}) \\in \\mathrm{L}^q(\\mathrm{X})$ for all $j$.}\n  It is shown that this statement is valid in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02895","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.02895","created_at":"2026-05-18T01:34:34.992337+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02895v2","created_at":"2026-05-18T01:34:34.992337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02895","created_at":"2026-05-18T01:34:34.992337+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZSITOWRQEYVZ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZSITOWRQEYVZI3B6","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZSITOWRQ","created_at":"2026-05-18T12:29:52.810259+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/ZSITOWRQEYVZI3B6V6OOEZRI4L","json":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L.json","graph_json":"https://pith.science/api/pith-number/ZSITOWRQEYVZI3B6V6OOEZRI4L/graph.json","events_json":"https://pith.science/api/pith-number/ZSITOWRQEYVZI3B6V6OOEZRI4L/events.json","paper":"https://pith.science/paper/ZSITOWRQ"},"agent_actions":{"view_html":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L","download_json":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L.json","view_paper":"https://pith.science/paper/ZSITOWRQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02895&json=true","fetch_graph":"https://pith.science/api/pith-number/ZSITOWRQEYVZI3B6V6OOEZRI4L/graph.json","fetch_events":"https://pith.science/api/pith-number/ZSITOWRQEYVZI3B6V6OOEZRI4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/action/storage_attestation","attest_author":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/action/author_attestation","sign_citation":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/action/citation_signature","submit_replication":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/action/replication_record"}},"created_at":"2026-05-18T01:34:34.992337+00:00","updated_at":"2026-05-18T01:34:34.992337+00:00"}