{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:KVAGQV3ENTA7O6F6XPO57B25X5","short_pith_number":"pith:KVAGQV3E","schema_version":"1.0","canonical_sha256":"55406857646cc1f778bebbdddf875dbf5c9b59b6dd090e6569638a18dfe7fb90","source":{"kind":"arxiv","id":"2506.08891","version":1},"attestation_state":"computed","paper":{"title":"The Fourier transform in variable exponent Lebesgue spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andr\\'e Pedroso Kowacs, Wagner Augusto Almeida de Moraes","submitted_at":"2025-06-10T15:17:33Z","abstract_excerpt":"In this work we define a Fourier transform for each $f\\in L^{p(\\cdot)}(\\mathbb{R})$, for a large class of exponent functions $p(\\cdot)$, as the distributional derivative of a H\\\"older continuous function. A norm is defined in the space of such Fourier transforms so that it is isometrically isomorphic to $L^{p(\\cdot)}(\\mathbb{R})$. We also prove several properties of this Fourier transform, such as inversion in norm and an exchange theorem."},"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":"2506.08891","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-06-10T15:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"19f42f25eb1c4877615a9de16768bcaf2d0980975b2967af0134020839f0e4d4","abstract_canon_sha256":"29f8b9977381c2306883ce1266caa1d1b053f231b05e6b3f93f8d0d95f78efeb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:14.831925Z","signature_b64":"fFW8oxxWhDaiORJh6wWVzKeGEfjeK/X0wrQ946xgRUy7Kgp1XDARjpFOnG5tj13IxKdzcGzWvz7Q/lnBoX0jBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55406857646cc1f778bebbdddf875dbf5c9b59b6dd090e6569638a18dfe7fb90","last_reissued_at":"2026-07-05T11:19:14.831512Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:14.831512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Fourier transform in variable exponent Lebesgue spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andr\\'e Pedroso Kowacs, Wagner Augusto Almeida de Moraes","submitted_at":"2025-06-10T15:17:33Z","abstract_excerpt":"In this work we define a Fourier transform for each $f\\in L^{p(\\cdot)}(\\mathbb{R})$, for a large class of exponent functions $p(\\cdot)$, as the distributional derivative of a H\\\"older continuous function. A norm is defined in the space of such Fourier transforms so that it is isometrically isomorphic to $L^{p(\\cdot)}(\\mathbb{R})$. We also prove several properties of this Fourier transform, such as inversion in norm and an exchange theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08891","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08891/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.08891","created_at":"2026-07-05T11:19:14.831585+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.08891v1","created_at":"2026-07-05T11:19:14.831585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08891","created_at":"2026-07-05T11:19:14.831585+00:00"},{"alias_kind":"pith_short_12","alias_value":"KVAGQV3ENTA7","created_at":"2026-07-05T11:19:14.831585+00:00"},{"alias_kind":"pith_short_16","alias_value":"KVAGQV3ENTA7O6F6","created_at":"2026-07-05T11:19:14.831585+00:00"},{"alias_kind":"pith_short_8","alias_value":"KVAGQV3E","created_at":"2026-07-05T11:19:14.831585+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/KVAGQV3ENTA7O6F6XPO57B25X5","json":"https://pith.science/pith/KVAGQV3ENTA7O6F6XPO57B25X5.json","graph_json":"https://pith.science/api/pith-number/KVAGQV3ENTA7O6F6XPO57B25X5/graph.json","events_json":"https://pith.science/api/pith-number/KVAGQV3ENTA7O6F6XPO57B25X5/events.json","paper":"https://pith.science/paper/KVAGQV3E"},"agent_actions":{"view_html":"https://pith.science/pith/KVAGQV3ENTA7O6F6XPO57B25X5","download_json":"https://pith.science/pith/KVAGQV3ENTA7O6F6XPO57B25X5.json","view_paper":"https://pith.science/paper/KVAGQV3E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.08891&json=true","fetch_graph":"https://pith.science/api/pith-number/KVAGQV3ENTA7O6F6XPO57B25X5/graph.json","fetch_events":"https://pith.science/api/pith-number/KVAGQV3ENTA7O6F6XPO57B25X5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KVAGQV3ENTA7O6F6XPO57B25X5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KVAGQV3ENTA7O6F6XPO57B25X5/action/storage_attestation","attest_author":"https://pith.science/pith/KVAGQV3ENTA7O6F6XPO57B25X5/action/author_attestation","sign_citation":"https://pith.science/pith/KVAGQV3ENTA7O6F6XPO57B25X5/action/citation_signature","submit_replication":"https://pith.science/pith/KVAGQV3ENTA7O6F6XPO57B25X5/action/replication_record"}},"created_at":"2026-07-05T11:19:14.831585+00:00","updated_at":"2026-07-05T11:19:14.831585+00:00"}