{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WJTUJPYRDFPM6XPXXYTLTDX7SU","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":"11b09572022a2662831b3d318624c440c9168337ad8fbad4e7f43f646543f159","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-10T15:12:23Z","title_canon_sha256":"29d1174246bc81bbfd5a3209f3ecabb735f218d99f092a4e6de9c68d011373d6"},"schema_version":"1.0","source":{"id":"1702.03201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03201","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03201v1","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03201","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"pith_short_12","alias_value":"WJTUJPYRDFPM","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WJTUJPYRDFPM6XPX","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WJTUJPYR","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:55ee6211afbc7237fc4ef119c7246368d2516af1ce72ea17d5142ce4d0b6d649","target":"graph","created_at":"2026-05-18T00:20:27Z","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 deal with kernel theorems for modulation spaces. We completely characterize the continuity of a linear operator on the modulation spaces $M^p$ for every $1\\leq p\\leq\\infty$, by the membership of its kernel to (mixed) modulation spaces. Whereas Feichtinger's kernel theorem (which we recapture as a special case) is the modulation space counterpart of Schwartz' kernel theorem for temperate distributions, our results do not have a couterpart in distribution theory. This reveals the superiority, in some respects, of the modulation space formalism upon distribution theory, as already emphasized i","authors_text":"Elena Cordero, Fabio Nicola","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-10T15:12:23Z","title":"Kernel theorems for modulation spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03201","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:ee9888ee848e1f7c4c35bd06c51237c8743bc3f5273ed3583a5f243e4a5c8bda","target":"record","created_at":"2026-05-18T00:20:27Z","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":"11b09572022a2662831b3d318624c440c9168337ad8fbad4e7f43f646543f159","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-10T15:12:23Z","title_canon_sha256":"29d1174246bc81bbfd5a3209f3ecabb735f218d99f092a4e6de9c68d011373d6"},"schema_version":"1.0","source":{"id":"1702.03201","kind":"arxiv","version":1}},"canonical_sha256":"b26744bf11195ecf5df7be26b98eff953bb140c7e330932d29e3fec35b8e677a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b26744bf11195ecf5df7be26b98eff953bb140c7e330932d29e3fec35b8e677a","first_computed_at":"2026-05-18T00:20:27.653397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:27.653397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KFf0VuTHyuQ86bWdfQbQJenE9PjMaQJg3daSQb/O6pkFQnA/O25fB9PJ8gz73F0mNCKPxgXVpphnK3MK0TyFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:27.654015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee9888ee848e1f7c4c35bd06c51237c8743bc3f5273ed3583a5f243e4a5c8bda","sha256:55ee6211afbc7237fc4ef119c7246368d2516af1ce72ea17d5142ce4d0b6d649"],"state_sha256":"4f64c4581af6bdfd4f336f3bcea1b983774de01451a1cf85dd994d3f3fc674c6"}