{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JMW2MQERU5PECQHIC377LB6VNA","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":"87a453a5aa1b84d518eeaf2af7469951b444645ac4c375242d31865ef71aa31c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-16T14:23:47Z","title_canon_sha256":"ad0e4b0f6e741a0cd85a4f8606d8418edfdeeb2357354112c27fe8d4b2e8ea0f"},"schema_version":"1.0","source":{"id":"1407.4321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4321","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4321v1","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4321","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"JMW2MQERU5PE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JMW2MQERU5PECQHI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JMW2MQER","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:c52d598735bac0454d47c8a2ca26bc7ea5215640eac485c3b48774c16ebee2f5","target":"graph","created_at":"2026-05-18T00:42:08Z","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":"Time-frequency localization operators are a quantization procedure that maps symbols on $R^{2d}$ to operators and depends on two window functions. We study the range of this quantization and its dependence on the window functions. If the short-time Fourier transform of the windows does not have any zero, then the range is dense in the Schatten $p$-classes. The main tool is new version of the Berezin transform associated to operators on $L^2(R^d)$. Although some results are analogous to results about Toeplitz operators on spaces of holomorphic functions, the absence of a complex structure requi","authors_text":"Dominik Bayer, Karlheinz Gr\\\"ochenig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-16T14:23:47Z","title":"Time-Frequency Localization Operators and a Berezin Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4321","kind":"arxiv","version":1},"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:a6df5a7e184d3c36b7281f969293b1e67dfdcd16f3e8d352be536a262c0ced85","target":"record","created_at":"2026-05-18T00:42:08Z","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":"87a453a5aa1b84d518eeaf2af7469951b444645ac4c375242d31865ef71aa31c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-16T14:23:47Z","title_canon_sha256":"ad0e4b0f6e741a0cd85a4f8606d8418edfdeeb2357354112c27fe8d4b2e8ea0f"},"schema_version":"1.0","source":{"id":"1407.4321","kind":"arxiv","version":1}},"canonical_sha256":"4b2da64091a75e4140e816fff587d5682fb361193fc2dc3ef604d404cebfff1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b2da64091a75e4140e816fff587d5682fb361193fc2dc3ef604d404cebfff1b","first_computed_at":"2026-05-18T00:42:08.044530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:08.044530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NKl8Vm/y/4RZz15OXR8dZh7hy/TeMqUMlr3XgOhG4vP3d92RLWp1DoiRUaCBa95IXYMduhnV8XX4y5r2E2ogAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:08.045088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6df5a7e184d3c36b7281f969293b1e67dfdcd16f3e8d352be536a262c0ced85","sha256:c52d598735bac0454d47c8a2ca26bc7ea5215640eac485c3b48774c16ebee2f5"],"state_sha256":"532b564c35463900e5e4358903726b413861c69fff6e41b86d23f5adcade7d07"}