{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:6T7YJM2VZY2KVDODFQPMENOFSV","short_pith_number":"pith:6T7YJM2V","schema_version":"1.0","canonical_sha256":"f4ff84b355ce34aa8dc32c1ec235c595667a93332d2dad4a4866990dc67db1f7","source":{"kind":"arxiv","id":"1004.1429","version":3},"attestation_state":"computed","paper":{"title":"Frames by Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Cabrelli, Peter Balazs, Sigrid Heineken, Ursula Molter","submitted_at":"2010-04-08T21:35:25Z","abstract_excerpt":"In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited function $h$ in $L^2(\\R^d)$. This is achieved by looking at a set of exponentials restricted to a set $E \\subset \\R^d$ with frequencies in a countable set $\\Lambda$ and multiplying it by the Fourier transform of a fixed function $h \\in L^2(E)$. Using density results due to Beurling, we prove the existence and give ways to construct frames by irregular translates."},"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":"1004.1429","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-04-08T21:35:25Z","cross_cats_sorted":[],"title_canon_sha256":"1998876bedffaa647c8b130dfd1cd50e5c059cc730d59e405c180a21e639a7a5","abstract_canon_sha256":"36a1ea88f24e7e2c09670920f06996db43b7058ee94cca88ae8e03219c3d63ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:39.652143Z","signature_b64":"Pos2oOO2duR7fWgpQp9auHF7dUkb1LDtGHnonupFugy25KOFgUqtvFuEpoVy/369b4k1jkoZUd5f84ugEmH0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4ff84b355ce34aa8dc32c1ec235c595667a93332d2dad4a4866990dc67db1f7","last_reissued_at":"2026-05-18T03:54:39.651650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:39.651650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frames by Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Cabrelli, Peter Balazs, Sigrid Heineken, Ursula Molter","submitted_at":"2010-04-08T21:35:25Z","abstract_excerpt":"In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited function $h$ in $L^2(\\R^d)$. This is achieved by looking at a set of exponentials restricted to a set $E \\subset \\R^d$ with frequencies in a countable set $\\Lambda$ and multiplying it by the Fourier transform of a fixed function $h \\in L^2(E)$. Using density results due to Beurling, we prove the existence and give ways to construct frames by irregular translates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1429","kind":"arxiv","version":3},"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":"1004.1429","created_at":"2026-05-18T03:54:39.651727+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.1429v3","created_at":"2026-05-18T03:54:39.651727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1429","created_at":"2026-05-18T03:54:39.651727+00:00"},{"alias_kind":"pith_short_12","alias_value":"6T7YJM2VZY2K","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"6T7YJM2VZY2KVDOD","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"6T7YJM2V","created_at":"2026-05-18T12:26:04.259169+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/6T7YJM2VZY2KVDODFQPMENOFSV","json":"https://pith.science/pith/6T7YJM2VZY2KVDODFQPMENOFSV.json","graph_json":"https://pith.science/api/pith-number/6T7YJM2VZY2KVDODFQPMENOFSV/graph.json","events_json":"https://pith.science/api/pith-number/6T7YJM2VZY2KVDODFQPMENOFSV/events.json","paper":"https://pith.science/paper/6T7YJM2V"},"agent_actions":{"view_html":"https://pith.science/pith/6T7YJM2VZY2KVDODFQPMENOFSV","download_json":"https://pith.science/pith/6T7YJM2VZY2KVDODFQPMENOFSV.json","view_paper":"https://pith.science/paper/6T7YJM2V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.1429&json=true","fetch_graph":"https://pith.science/api/pith-number/6T7YJM2VZY2KVDODFQPMENOFSV/graph.json","fetch_events":"https://pith.science/api/pith-number/6T7YJM2VZY2KVDODFQPMENOFSV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6T7YJM2VZY2KVDODFQPMENOFSV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6T7YJM2VZY2KVDODFQPMENOFSV/action/storage_attestation","attest_author":"https://pith.science/pith/6T7YJM2VZY2KVDODFQPMENOFSV/action/author_attestation","sign_citation":"https://pith.science/pith/6T7YJM2VZY2KVDODFQPMENOFSV/action/citation_signature","submit_replication":"https://pith.science/pith/6T7YJM2VZY2KVDODFQPMENOFSV/action/replication_record"}},"created_at":"2026-05-18T03:54:39.651727+00:00","updated_at":"2026-05-18T03:54:39.651727+00:00"}