{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7QYSHE5PJ6B6VSM63CJ3QHVCAS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"237c3eec79f60e39e8b300b94fa562356a0169de4d736ca1cdf49373503ef4fb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2009-03-03T23:06:34Z","title_canon_sha256":"d54d643f8b734d6b90e4eb024886b3effbd80b1d18e3bff42b6ca2ecfda1e42c"},"schema_version":"1.0","source":{"id":"0903.0651","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.0651","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"0903.0651v3","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.0651","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"7QYSHE5PJ6B6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7QYSHE5PJ6B6VSM6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7QYSHE5P","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:3ab5772448c657569bf1a5e363965fe463ff7596d76128fe7fcdbec090f277e8","target":"graph","created_at":"2026-05-18T04:42:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the weighted Bergman spaces HL^2(B^d,\\mu_{\\lambda}), where d\\mu_\\lambda(z)=c_{\\lambda}(1-|z|^2)^lambda d\\tau, \\tau being the hyperbolic volume measure. These spaces are nonzero if and only if \\lambda>d. For 0<\\lambda\\leq d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert--Schmidt operators on t","authors_text":"Brian C. Hall, Kamthorn Chailuek","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2009-03-03T23:06:34Z","title":"Toeplitz operators on generalized Bergman spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0651","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:832d09a20a1a4e6013467853b6c67c7b2740f77a8da11528daeacabd85cd38d3","target":"record","created_at":"2026-05-18T04:42:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"237c3eec79f60e39e8b300b94fa562356a0169de4d736ca1cdf49373503ef4fb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2009-03-03T23:06:34Z","title_canon_sha256":"d54d643f8b734d6b90e4eb024886b3effbd80b1d18e3bff42b6ca2ecfda1e42c"},"schema_version":"1.0","source":{"id":"0903.0651","kind":"arxiv","version":3}},"canonical_sha256":"fc312393af4f83eac99ed893b81ea20489bb07082c8903c49d22cd29ad3c8811","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc312393af4f83eac99ed893b81ea20489bb07082c8903c49d22cd29ad3c8811","first_computed_at":"2026-05-18T04:42:35.370739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:35.370739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hXdu0k5gWYVm4sKsVMCi+Qwq/yzNXxKpa44v5VuS/73a5GhiVYrcxXquhValLK5P4AxiZnoLGyv1mJfRdS4aBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:35.371521Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.0651","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:832d09a20a1a4e6013467853b6c67c7b2740f77a8da11528daeacabd85cd38d3","sha256:3ab5772448c657569bf1a5e363965fe463ff7596d76128fe7fcdbec090f277e8"],"state_sha256":"38bdd8e959131a7dd9a529086f4c99074ecacb76904a0a503d58463a27d46148"}