{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GS4CDIBIMQ2VBY6I247HMNVUOF","short_pith_number":"pith:GS4CDIBI","schema_version":"1.0","canonical_sha256":"34b821a028643550e3c8d73e7636b47158262292be1fc62b6ce9cc9d349627be","source":{"kind":"arxiv","id":"1806.06816","version":1},"attestation_state":"computed","paper":{"title":"$C_0$-semigroups of 2-isometries and Dirichlet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Eva A. Gallardo-Guti\\'errez, Jonathan R. Partington","submitted_at":"2018-06-18T16:45:47Z","abstract_excerpt":"In the context of a theorem of Richter, we establish a similarity between $C_0$-semigroups of analytic 2-isometries $\\{T(t)\\}_{t\\geq0}$ acting on a Hilbert space $\\mathcal H$ and the multiplication operator semigroup $\\{M_{\\phi_t}\\}_{t\\geq 0}$ induced by $\\phi_t(s)=\\exp (-st)$ for $s$ in the right-half plane $\\mathbb{C}_+$ acting boundedly on weighted Dirichlet spaces on $\\mathbb{C}_+$. As a consequence, we derive a connection with the right shift semigroup $\\{S_t\\}_{t\\geq 0}$ $$ S_tf(x)=\\left \\{ \\begin{array}{ll} 0 & \\mbox { if }0\\leq t\\leq x, \\\\ f(x-t)& \\mbox { if } x>t, \\end{array} \\right ."},"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":"1806.06816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-18T16:45:47Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"47081c124f7e52f33b920caa7aba50359c85631d0e17e82f691ddff571aa408b","abstract_canon_sha256":"23f71cb3f44f5eda5f0790b9744270a4923049dcce889ea9659710ef57765755"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:59.044559Z","signature_b64":"fVUXRRsw7RddPTN260wO+17urHQjly3sBZj4wphPSwx64RAS0exTPoOksWhmCVJ72r+0YQXmC7awAb7hAD7dBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34b821a028643550e3c8d73e7636b47158262292be1fc62b6ce9cc9d349627be","last_reissued_at":"2026-05-18T00:12:59.044094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:59.044094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$C_0$-semigroups of 2-isometries and Dirichlet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Eva A. Gallardo-Guti\\'errez, Jonathan R. Partington","submitted_at":"2018-06-18T16:45:47Z","abstract_excerpt":"In the context of a theorem of Richter, we establish a similarity between $C_0$-semigroups of analytic 2-isometries $\\{T(t)\\}_{t\\geq0}$ acting on a Hilbert space $\\mathcal H$ and the multiplication operator semigroup $\\{M_{\\phi_t}\\}_{t\\geq 0}$ induced by $\\phi_t(s)=\\exp (-st)$ for $s$ in the right-half plane $\\mathbb{C}_+$ acting boundedly on weighted Dirichlet spaces on $\\mathbb{C}_+$. As a consequence, we derive a connection with the right shift semigroup $\\{S_t\\}_{t\\geq 0}$ $$ S_tf(x)=\\left \\{ \\begin{array}{ll} 0 & \\mbox { if }0\\leq t\\leq x, \\\\ f(x-t)& \\mbox { if } x>t, \\end{array} \\right ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06816","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":"1806.06816","created_at":"2026-05-18T00:12:59.044158+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.06816v1","created_at":"2026-05-18T00:12:59.044158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06816","created_at":"2026-05-18T00:12:59.044158+00:00"},{"alias_kind":"pith_short_12","alias_value":"GS4CDIBIMQ2V","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GS4CDIBIMQ2VBY6I","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GS4CDIBI","created_at":"2026-05-18T12:32:25.280505+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/GS4CDIBIMQ2VBY6I247HMNVUOF","json":"https://pith.science/pith/GS4CDIBIMQ2VBY6I247HMNVUOF.json","graph_json":"https://pith.science/api/pith-number/GS4CDIBIMQ2VBY6I247HMNVUOF/graph.json","events_json":"https://pith.science/api/pith-number/GS4CDIBIMQ2VBY6I247HMNVUOF/events.json","paper":"https://pith.science/paper/GS4CDIBI"},"agent_actions":{"view_html":"https://pith.science/pith/GS4CDIBIMQ2VBY6I247HMNVUOF","download_json":"https://pith.science/pith/GS4CDIBIMQ2VBY6I247HMNVUOF.json","view_paper":"https://pith.science/paper/GS4CDIBI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.06816&json=true","fetch_graph":"https://pith.science/api/pith-number/GS4CDIBIMQ2VBY6I247HMNVUOF/graph.json","fetch_events":"https://pith.science/api/pith-number/GS4CDIBIMQ2VBY6I247HMNVUOF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GS4CDIBIMQ2VBY6I247HMNVUOF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GS4CDIBIMQ2VBY6I247HMNVUOF/action/storage_attestation","attest_author":"https://pith.science/pith/GS4CDIBIMQ2VBY6I247HMNVUOF/action/author_attestation","sign_citation":"https://pith.science/pith/GS4CDIBIMQ2VBY6I247HMNVUOF/action/citation_signature","submit_replication":"https://pith.science/pith/GS4CDIBIMQ2VBY6I247HMNVUOF/action/replication_record"}},"created_at":"2026-05-18T00:12:59.044158+00:00","updated_at":"2026-05-18T00:12:59.044158+00:00"}