{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3TZDSD6BOR4XHZG2XSUU5SXOQQ","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":"e1bedb2e98b4cefe51def7401f7dc388cb131330a05848ab082356316dfe267b","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-09T10:00:29Z","title_canon_sha256":"8d17812ed282c46e6b6bb417d1b16ec0ecbe8f528248631df336861a939c0c3c"},"schema_version":"1.0","source":{"id":"1705.03253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03253","created_at":"2026-05-18T00:32:55Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03253v2","created_at":"2026-05-18T00:32:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03253","created_at":"2026-05-18T00:32:55Z"},{"alias_kind":"pith_short_12","alias_value":"3TZDSD6BOR4X","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3TZDSD6BOR4XHZG2","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3TZDSD6B","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:cb0842d0db68c2fc51d87d1afc4f992cbb0337bc94938448e3e8a00a7f58896e","target":"graph","created_at":"2026-05-18T00:32:55Z","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":"Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of localization operators which is complemented by an appropriate Fourier transform, the Fourier-Wigner transform. We use Lieb's uncertainty principle to establish a sharp Hausdorff-Young inequality for the Fourier-Wigner transform. Noncommutative Tauberian theorems due to Werner allow us to extend results of Bayer and Gr\\\"ochenig on localization operators. Furthermore w","authors_text":"Eirik Skrettingland, Franz Luef","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-09T10:00:29Z","title":"Convolutions for localization operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03253","kind":"arxiv","version":2},"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:d1685ad8c7afea09443636c884cad9520e97bc88fa72256c4640a404c3b45d25","target":"record","created_at":"2026-05-18T00:32:55Z","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":"e1bedb2e98b4cefe51def7401f7dc388cb131330a05848ab082356316dfe267b","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-09T10:00:29Z","title_canon_sha256":"8d17812ed282c46e6b6bb417d1b16ec0ecbe8f528248631df336861a939c0c3c"},"schema_version":"1.0","source":{"id":"1705.03253","kind":"arxiv","version":2}},"canonical_sha256":"dcf2390fc1747973e4dabca94ecaee8422e133dfb5ab894467d90f25ca0ac35a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcf2390fc1747973e4dabca94ecaee8422e133dfb5ab894467d90f25ca0ac35a","first_computed_at":"2026-05-18T00:32:55.162509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:55.162509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wPe+URfxOhlFE4rUguZVUhMZGZS+YhwqHTGZQrlPUvrc6Fxd8EBt0ueaLXZZ0+GHacMbNIV6BJuZjdnsQNlDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:55.163189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1685ad8c7afea09443636c884cad9520e97bc88fa72256c4640a404c3b45d25","sha256:cb0842d0db68c2fc51d87d1afc4f992cbb0337bc94938448e3e8a00a7f58896e"],"state_sha256":"b8d684861dbfc7b89e34af035b6d2dd1917fa2e3af87ed83ef13b6fe3f0b3c7f"}