{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QDKUOXKSGNPGPUJQYH6O22WGWK","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":"8c3a618270879c4631b806cdb090444aa45ce44be13f2d5cc78e98e3c51223eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-09T11:55:21Z","title_canon_sha256":"5fd5eb7f4392b0181a24411e2993f7c5bcef5a4f3ebbd8a431d3e8afe1c8346d"},"schema_version":"1.0","source":{"id":"0904.1508","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.1508","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"0904.1508v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1508","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"QDKUOXKSGNPG","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QDKUOXKSGNPGPUJQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QDKUOXKS","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:9647e6dc83a207978dacbc0ae99afa88f5a825299c44950d932f14156c88b8e8","target":"graph","created_at":"2026-05-18T01:11:55Z","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":"We completely characterize the boundedness on $L^p$ spaces and on Wiener amalgam spaces of the short-time Fourier transform (STFT) and of a special class of pseudodifferential operators, called localization operators. Precisely, a well-known STFT boundedness result on $L^p$ spaces is proved to be sharp. Then, sufficient conditions for the STFT to be bounded on the Wiener amalgam spaces $W(L^p,L^q)$ are given and their sharpness is shown. Localization operators are treated similarly. Using different techniques from those employed in the literature, we relax the known sufficient boundedness cond","authors_text":"Elena Cordero, Fabio Nicola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-09T11:55:21Z","title":"Sharp Continuity Results for the Short-Time Fourier Transform and for Localization Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1508","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":"sha256:6c8d3b3b4c9fd97030e9f1372ae3a56dc9b3a40e2aee6a1f6beeab0fdbf7deea","target":"record","created_at":"2026-05-18T01:11:55Z","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":"8c3a618270879c4631b806cdb090444aa45ce44be13f2d5cc78e98e3c51223eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-09T11:55:21Z","title_canon_sha256":"5fd5eb7f4392b0181a24411e2993f7c5bcef5a4f3ebbd8a431d3e8afe1c8346d"},"schema_version":"1.0","source":{"id":"0904.1508","kind":"arxiv","version":2}},"canonical_sha256":"80d5475d52335e67d130c1fced6ac6b2bca60d4cdc5ef8a301b2e038d6f9944a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80d5475d52335e67d130c1fced6ac6b2bca60d4cdc5ef8a301b2e038d6f9944a","first_computed_at":"2026-05-18T01:11:55.638015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.638015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iNF1xHcawnXeba4m6Zqbk+DSjckvJ001ztRuIbw2ZbhCloEAqGI9juyevYt3UOD/AlwTcY77jdNB4nCqtON0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.638358Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.1508","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c8d3b3b4c9fd97030e9f1372ae3a56dc9b3a40e2aee6a1f6beeab0fdbf7deea","sha256:9647e6dc83a207978dacbc0ae99afa88f5a825299c44950d932f14156c88b8e8"],"state_sha256":"c7cd0c366ac00e8074a9ce52e37a11ec7e03474750c9e5a26ac3324d57bc8d4c"}