{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GVIA5UM3IO2DTIL6NCW7YZ2G5Y","short_pith_number":"pith:GVIA5UM3","schema_version":"1.0","canonical_sha256":"35500ed19b43b439a17e68adfc6746ee399343e314d1cb539eef44bc84238906","source":{"kind":"arxiv","id":"1304.4922","version":1},"attestation_state":"computed","paper":{"title":"An invitation to harmonic analysis associated with semigroups of operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.CA","authors_text":"Javier Parcet, Marius Junge, Tao Mei","submitted_at":"2013-04-17T19:15:40Z","abstract_excerpt":"This article is an introduction to our recent work in harmonic analysis associated with semigroups of operators, in the effort of finding a noncommutative Calder\\'on-Zygmund theory for von Neumann algebras. The classical CZ theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of such metrics -or with very little information on the metric- Markov semigroups of operators appear to be the right substitutes of classical metric/geometric tools in harmonic analysis. Our approach is particularly useful in the noncommutative setting "},"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":"1304.4922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-17T19:15:40Z","cross_cats_sorted":["math.FA","math.OA"],"title_canon_sha256":"75e95ad3f8d0cf52a5559eace81e820e81d7c37076e1b2ab4dc79d117fe64907","abstract_canon_sha256":"3aa11900feb874485ce5b06593098c162816438a1837c251b748a309c3574ea5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:43.183826Z","signature_b64":"ZbiKfpGbry7d8w2Fvwa7JKcfmQPHsHF32rGaPE3VCbw66asovy5Bg2cZJRYnNcQV+BXFupEJmbF0O+qoXN7zCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35500ed19b43b439a17e68adfc6746ee399343e314d1cb539eef44bc84238906","last_reissued_at":"2026-05-18T03:27:43.183102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:43.183102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An invitation to harmonic analysis associated with semigroups of operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.CA","authors_text":"Javier Parcet, Marius Junge, Tao Mei","submitted_at":"2013-04-17T19:15:40Z","abstract_excerpt":"This article is an introduction to our recent work in harmonic analysis associated with semigroups of operators, in the effort of finding a noncommutative Calder\\'on-Zygmund theory for von Neumann algebras. The classical CZ theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of such metrics -or with very little information on the metric- Markov semigroups of operators appear to be the right substitutes of classical metric/geometric tools in harmonic analysis. Our approach is particularly useful in the noncommutative setting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4922","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":"1304.4922","created_at":"2026-05-18T03:27:43.183241+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4922v1","created_at":"2026-05-18T03:27:43.183241+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4922","created_at":"2026-05-18T03:27:43.183241+00:00"},{"alias_kind":"pith_short_12","alias_value":"GVIA5UM3IO2D","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GVIA5UM3IO2DTIL6","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GVIA5UM3","created_at":"2026-05-18T12:27:45.050594+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/GVIA5UM3IO2DTIL6NCW7YZ2G5Y","json":"https://pith.science/pith/GVIA5UM3IO2DTIL6NCW7YZ2G5Y.json","graph_json":"https://pith.science/api/pith-number/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/graph.json","events_json":"https://pith.science/api/pith-number/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/events.json","paper":"https://pith.science/paper/GVIA5UM3"},"agent_actions":{"view_html":"https://pith.science/pith/GVIA5UM3IO2DTIL6NCW7YZ2G5Y","download_json":"https://pith.science/pith/GVIA5UM3IO2DTIL6NCW7YZ2G5Y.json","view_paper":"https://pith.science/paper/GVIA5UM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4922&json=true","fetch_graph":"https://pith.science/api/pith-number/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/graph.json","fetch_events":"https://pith.science/api/pith-number/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/action/storage_attestation","attest_author":"https://pith.science/pith/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/action/author_attestation","sign_citation":"https://pith.science/pith/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/action/citation_signature","submit_replication":"https://pith.science/pith/GVIA5UM3IO2DTIL6NCW7YZ2G5Y/action/replication_record"}},"created_at":"2026-05-18T03:27:43.183241+00:00","updated_at":"2026-05-18T03:27:43.183241+00:00"}