{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GSOJYV4FYANMEMHSDMRRBAPXYR","short_pith_number":"pith:GSOJYV4F","schema_version":"1.0","canonical_sha256":"349c9c5785c01ac230f21b231081f7c4691d57d3e8153e97166213111db67f61","source":{"kind":"arxiv","id":"1404.4298","version":1},"attestation_state":"computed","paper":{"title":"Wavelet Coorbit Spaces viewed as Decomposition Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Felix Voigtlaender, Hartmut F\\\"uhr","submitted_at":"2014-04-16T16:09:14Z","abstract_excerpt":"In this paper we show that the Fourier transform induces an isomorphism between the coorbit spaces defined by Feichtinger and Gr\\\"ochenig of the mixed, weighted Lebesgue spaces $L_{v}^{p,q}$ with respect to the quasi-regular representation of a semi-direct product $\\mathbb{R}^{d}\\rtimes H$ with suitably chosen dilation group $H$, and certain decomposition spaces $\\mathcal{D}\\left(\\mathcal{Q},L^{p},\\ell_{u}^{q}\\right)$ (essentially as introduced by Feichtinger and Gr\\\"obner), where the localized ,,parts`` of a function are measured in the $\\mathcal{F}L^{p}$-norm.\n  This equivalence is useful in"},"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":"1404.4298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-16T16:09:14Z","cross_cats_sorted":[],"title_canon_sha256":"02ab40414f94d3bd0688756416307cadf2a7b0d5855e683688965620edc4560f","abstract_canon_sha256":"e7288cbc0d08785fee16308082a7c9a9e43e9820e1ea886acbb8d97924daf3fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:05.730836Z","signature_b64":"4I+xMbpzLSguSmODIQ62M5iFX4YfWVF0UdCQS78S5SIJ490nGZCtRdUrgWixie+fZa302Tx4aJGL67IjlSlPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"349c9c5785c01ac230f21b231081f7c4691d57d3e8153e97166213111db67f61","last_reissued_at":"2026-05-18T02:54:05.730202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:05.730202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wavelet Coorbit Spaces viewed as Decomposition Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Felix Voigtlaender, Hartmut F\\\"uhr","submitted_at":"2014-04-16T16:09:14Z","abstract_excerpt":"In this paper we show that the Fourier transform induces an isomorphism between the coorbit spaces defined by Feichtinger and Gr\\\"ochenig of the mixed, weighted Lebesgue spaces $L_{v}^{p,q}$ with respect to the quasi-regular representation of a semi-direct product $\\mathbb{R}^{d}\\rtimes H$ with suitably chosen dilation group $H$, and certain decomposition spaces $\\mathcal{D}\\left(\\mathcal{Q},L^{p},\\ell_{u}^{q}\\right)$ (essentially as introduced by Feichtinger and Gr\\\"obner), where the localized ,,parts`` of a function are measured in the $\\mathcal{F}L^{p}$-norm.\n  This equivalence is useful in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4298","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":"1404.4298","created_at":"2026-05-18T02:54:05.730293+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4298v1","created_at":"2026-05-18T02:54:05.730293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4298","created_at":"2026-05-18T02:54:05.730293+00:00"},{"alias_kind":"pith_short_12","alias_value":"GSOJYV4FYANM","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GSOJYV4FYANMEMHS","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GSOJYV4F","created_at":"2026-05-18T12:28:30.664211+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/GSOJYV4FYANMEMHSDMRRBAPXYR","json":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR.json","graph_json":"https://pith.science/api/pith-number/GSOJYV4FYANMEMHSDMRRBAPXYR/graph.json","events_json":"https://pith.science/api/pith-number/GSOJYV4FYANMEMHSDMRRBAPXYR/events.json","paper":"https://pith.science/paper/GSOJYV4F"},"agent_actions":{"view_html":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR","download_json":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR.json","view_paper":"https://pith.science/paper/GSOJYV4F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4298&json=true","fetch_graph":"https://pith.science/api/pith-number/GSOJYV4FYANMEMHSDMRRBAPXYR/graph.json","fetch_events":"https://pith.science/api/pith-number/GSOJYV4FYANMEMHSDMRRBAPXYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/action/storage_attestation","attest_author":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/action/author_attestation","sign_citation":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/action/citation_signature","submit_replication":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/action/replication_record"}},"created_at":"2026-05-18T02:54:05.730293+00:00","updated_at":"2026-05-18T02:54:05.730293+00:00"}