{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EEB3WDGLX23M2WUZXJE47R5UXE","short_pith_number":"pith:EEB3WDGL","schema_version":"1.0","canonical_sha256":"2103bb0ccbbeb6cd5a99ba49cfc7b4b92acb84fb51321938591726f533a0b864","source":{"kind":"arxiv","id":"1707.06862","version":1},"attestation_state":"computed","paper":{"title":"A characterization of modulation spaces by symplectic rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Elena Cordero, Fabio Nicola, Maurice de Gosson","submitted_at":"2017-07-21T12:12:29Z","abstract_excerpt":"This note contains a new characterization of modulation spaces $M^p(\\mathbb{R}^n)$, $1\\leq p\\leq \\infty$, by symplectic rotations. Precisely, instead to measure the time-frequency content of a function by using translations and modulations of a fixed window as building blocks, we use translations and metaplectic operators corresponding to symplectic rotations. Technically, this amounts to replace, in the computation of the $M^p(\\mathbb{R}^n)$-norm, the integral in the time-frequency plane with an integral on $\\mathbb{R}^n\\times U(2n,\\mathbb{R})$ with respect to a suitable measure, $U(2n,\\mathb"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.06862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-21T12:12:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"371db504c3f1ed2d57398262f3f61778d7a8c81ebd63145a56d016439ad535f6","abstract_canon_sha256":"00d7c284ce338eea7230a8a5cedd6003517eddec439e402f84191b2d48acb305"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:51.322595Z","signature_b64":"jmW4VwLPKo08daWvJTx4EdRTvFuK88oMPN3W16dtJjXmQXfikEa1XGhp0EUM8wF6mVY/tCvGndOH6UWrQA2PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2103bb0ccbbeb6cd5a99ba49cfc7b4b92acb84fb51321938591726f533a0b864","last_reissued_at":"2026-05-18T00:39:51.322035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:51.322035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of modulation spaces by symplectic rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Elena Cordero, Fabio Nicola, Maurice de Gosson","submitted_at":"2017-07-21T12:12:29Z","abstract_excerpt":"This note contains a new characterization of modulation spaces $M^p(\\mathbb{R}^n)$, $1\\leq p\\leq \\infty$, by symplectic rotations. Precisely, instead to measure the time-frequency content of a function by using translations and modulations of a fixed window as building blocks, we use translations and metaplectic operators corresponding to symplectic rotations. Technically, this amounts to replace, in the computation of the $M^p(\\mathbb{R}^n)$-norm, the integral in the time-frequency plane with an integral on $\\mathbb{R}^n\\times U(2n,\\mathbb{R})$ with respect to a suitable measure, $U(2n,\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06862","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.06862","created_at":"2026-05-18T00:39:51.322142+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06862v1","created_at":"2026-05-18T00:39:51.322142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06862","created_at":"2026-05-18T00:39:51.322142+00:00"},{"alias_kind":"pith_short_12","alias_value":"EEB3WDGLX23M","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EEB3WDGLX23M2WUZ","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EEB3WDGL","created_at":"2026-05-18T12:31:12.930513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE","json":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE.json","graph_json":"https://pith.science/api/pith-number/EEB3WDGLX23M2WUZXJE47R5UXE/graph.json","events_json":"https://pith.science/api/pith-number/EEB3WDGLX23M2WUZXJE47R5UXE/events.json","paper":"https://pith.science/paper/EEB3WDGL"},"agent_actions":{"view_html":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE","download_json":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE.json","view_paper":"https://pith.science/paper/EEB3WDGL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06862&json=true","fetch_graph":"https://pith.science/api/pith-number/EEB3WDGLX23M2WUZXJE47R5UXE/graph.json","fetch_events":"https://pith.science/api/pith-number/EEB3WDGLX23M2WUZXJE47R5UXE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE/action/storage_attestation","attest_author":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE/action/author_attestation","sign_citation":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE/action/citation_signature","submit_replication":"https://pith.science/pith/EEB3WDGLX23M2WUZXJE47R5UXE/action/replication_record"}},"created_at":"2026-05-18T00:39:51.322142+00:00","updated_at":"2026-05-18T00:39:51.322142+00:00"}