{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:24MOJK755SHMZLPA7KWZYHP7AC","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":"3a05bf89d519d0f58386b70989623d9afc9cf979c6902d82a12f9433b2494daa","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-08-31T01:37:28Z","title_canon_sha256":"a28a9afd4fbe8423ba8b31c7a1fdfbff5ee019baf7cd104f65b19ef76f290027"},"schema_version":"1.0","source":{"id":"1108.6108","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6108","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6108v2","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6108","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"24MOJK755SHM","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"24MOJK755SHMZLPA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"24MOJK75","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:85bfd9d74b586032888634c53771e80cb314a067f01e068df0e0a2b9c387e657","target":"graph","created_at":"2026-05-18T02:32:14Z","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 show that multi-window Gabor frames with windows in the Wiener algebra $W(L^{\\infty}, \\ell^{1})$ are Banach frames for all Wiener amalgam spaces. As a byproduct of our results we positively answer an open question that was posed by [Krishtal and Okoudjou, Invertibility of the Gabor frame operator on the Wiener amalgam space, J. Approx. Theory, 153(2), 2008] and concerns the continuity of the canonical dual of a Gabor frame with a continuous generator in the Wiener algebra. The proofs are based on a recent version of Wiener's $1/f$ lemma.","authors_text":"Ilya A. Krishtal, Jens G. Christensen, Jos\\'e Luis Romero, Kasso A. Okoudjou, Radu Balan","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-08-31T01:37:28Z","title":"Multi-window Gabor frames in amalgam spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6108","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":"sha256:72eb378644561a23b9660a8040e76f49937a9f20978dbe59e3ca97ede54022c5","target":"record","created_at":"2026-05-18T02:32:14Z","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":"3a05bf89d519d0f58386b70989623d9afc9cf979c6902d82a12f9433b2494daa","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-08-31T01:37:28Z","title_canon_sha256":"a28a9afd4fbe8423ba8b31c7a1fdfbff5ee019baf7cd104f65b19ef76f290027"},"schema_version":"1.0","source":{"id":"1108.6108","kind":"arxiv","version":2}},"canonical_sha256":"d718e4abfdec8eccade0faad9c1dff00b0d7b22de46813951f59a395529d5b4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d718e4abfdec8eccade0faad9c1dff00b0d7b22de46813951f59a395529d5b4b","first_computed_at":"2026-05-18T02:32:14.790923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:14.790923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CLK96FfzZde/wF1K764aocBhXTVRZ0dRzrNTd9PP/KABkhRYdDoImBzN6n/hdWVnV5f446NgoDuqraGyrksvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:14.791613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.6108","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72eb378644561a23b9660a8040e76f49937a9f20978dbe59e3ca97ede54022c5","sha256:85bfd9d74b586032888634c53771e80cb314a067f01e068df0e0a2b9c387e657"],"state_sha256":"05a758241d3a82162437dfe86270305cc27df15388d6c8d77eab3870b6dd7864"}