{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YMFOF76CNSXLUVZYMQHIXO5LS6","short_pith_number":"pith:YMFOF76C","schema_version":"1.0","canonical_sha256":"c30ae2ffc26caeba5738640e8bbbab97b05be091f66c314a6e2ba29622e52665","source":{"kind":"arxiv","id":"1111.7294","version":1},"attestation_state":"computed","paper":{"title":"Boundedness and compactness of composition operators on Segal-Bargmann spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Trieu Le","submitted_at":"2011-11-30T20:05:04Z","abstract_excerpt":"For $E$ a Hilbert space, let $\\mathcal{H}(E)$ denote the Segal-Bargmann space (also known as the Fock space) over $E$, which is a reproducing kernel Hilbert space with kernel $K(x,y)=\\exp(< x,y>)$ for $x,y$ in $E$. If $\\phi$ is a mapping on $E$, the composition operator $C_{\\phi}$ is defined by $C_{\\phi}h = h\\circ\\phi$ for $h\\in \\mathcal{H}(E)$ for which $h\\circ\\phi$ also belongs to $\\mathcal{H}(E)$. We determine necessary and sufficient conditions for the boundedness and compactness of $C_{\\phi}$. Our results generalize results obtained earlier by Carswell, MacCluer and Schuster for finite di"},"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":"1111.7294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-11-30T20:05:04Z","cross_cats_sorted":[],"title_canon_sha256":"83f068a33c2b7b0bc4b043aae004af9498c5bdf4e6ae1367290ff4c401818f2e","abstract_canon_sha256":"cc16c3f299fb612cc426ef9ef41fca0565b18eab746fafbdaf81ecbf527f62f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:18.202174Z","signature_b64":"nWxUWcc3NTAFEOMepMhGivFccHXJcwwg8ADrUpHUGrdvtLNdywacWcrpE+5C0H2EQY6BaVhJe5hFoh7D3xo+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c30ae2ffc26caeba5738640e8bbbab97b05be091f66c314a6e2ba29622e52665","last_reissued_at":"2026-05-18T04:07:18.201519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:18.201519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundedness and compactness of composition operators on Segal-Bargmann spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Trieu Le","submitted_at":"2011-11-30T20:05:04Z","abstract_excerpt":"For $E$ a Hilbert space, let $\\mathcal{H}(E)$ denote the Segal-Bargmann space (also known as the Fock space) over $E$, which is a reproducing kernel Hilbert space with kernel $K(x,y)=\\exp(< x,y>)$ for $x,y$ in $E$. If $\\phi$ is a mapping on $E$, the composition operator $C_{\\phi}$ is defined by $C_{\\phi}h = h\\circ\\phi$ for $h\\in \\mathcal{H}(E)$ for which $h\\circ\\phi$ also belongs to $\\mathcal{H}(E)$. We determine necessary and sufficient conditions for the boundedness and compactness of $C_{\\phi}$. Our results generalize results obtained earlier by Carswell, MacCluer and Schuster for finite di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7294","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":"1111.7294","created_at":"2026-05-18T04:07:18.201618+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.7294v1","created_at":"2026-05-18T04:07:18.201618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7294","created_at":"2026-05-18T04:07:18.201618+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMFOF76CNSXL","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMFOF76CNSXLUVZY","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMFOF76C","created_at":"2026-05-18T12:26:47.523578+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/YMFOF76CNSXLUVZYMQHIXO5LS6","json":"https://pith.science/pith/YMFOF76CNSXLUVZYMQHIXO5LS6.json","graph_json":"https://pith.science/api/pith-number/YMFOF76CNSXLUVZYMQHIXO5LS6/graph.json","events_json":"https://pith.science/api/pith-number/YMFOF76CNSXLUVZYMQHIXO5LS6/events.json","paper":"https://pith.science/paper/YMFOF76C"},"agent_actions":{"view_html":"https://pith.science/pith/YMFOF76CNSXLUVZYMQHIXO5LS6","download_json":"https://pith.science/pith/YMFOF76CNSXLUVZYMQHIXO5LS6.json","view_paper":"https://pith.science/paper/YMFOF76C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.7294&json=true","fetch_graph":"https://pith.science/api/pith-number/YMFOF76CNSXLUVZYMQHIXO5LS6/graph.json","fetch_events":"https://pith.science/api/pith-number/YMFOF76CNSXLUVZYMQHIXO5LS6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMFOF76CNSXLUVZYMQHIXO5LS6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMFOF76CNSXLUVZYMQHIXO5LS6/action/storage_attestation","attest_author":"https://pith.science/pith/YMFOF76CNSXLUVZYMQHIXO5LS6/action/author_attestation","sign_citation":"https://pith.science/pith/YMFOF76CNSXLUVZYMQHIXO5LS6/action/citation_signature","submit_replication":"https://pith.science/pith/YMFOF76CNSXLUVZYMQHIXO5LS6/action/replication_record"}},"created_at":"2026-05-18T04:07:18.201618+00:00","updated_at":"2026-05-18T04:07:18.201618+00:00"}