{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QLYJXM4LRFNRASOJVO7DB5CSP7","short_pith_number":"pith:QLYJXM4L","schema_version":"1.0","canonical_sha256":"82f09bb38b895b1049c9abbe30f4527ffb78e290fcace7e9b3e2de0ce11fdbe5","source":{"kind":"arxiv","id":"1203.0506","version":1},"attestation_state":"computed","paper":{"title":"Frames, semi-frames, and Hilbert scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J-P. Antoine, P. Balazs","submitted_at":"2012-03-02T16:09:39Z","abstract_excerpt":"Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded inverse, whereas a lower semi-frame has an unbounded frame operator, with bounded inverse. For upper semi-frames, in the discrete and the continuous case, we build two natural Hilbert scales which may yield a novel characterization of certain function spaces of interest in signal processing. We present some examples and, in addition, some results concerning the du"},"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":"1203.0506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-02T16:09:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a9a3126fef155ae377352720460f075f63860a36500b42205131e1a55be8270e","abstract_canon_sha256":"ff71f89862b3b6069abb26c977b95f4f799bbcaf38bb98e1172c7142ec75b7e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:28.511873Z","signature_b64":"cJhggjzruyp246/81IwNw7PNwlobEoLgiLIncMXPkTuBaBSrW3sWDzR46LdpVxQQKP3SS0U7wE87X0SMYPbqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82f09bb38b895b1049c9abbe30f4527ffb78e290fcace7e9b3e2de0ce11fdbe5","last_reissued_at":"2026-05-18T03:43:28.511413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:28.511413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frames, semi-frames, and Hilbert scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J-P. Antoine, P. Balazs","submitted_at":"2012-03-02T16:09:39Z","abstract_excerpt":"Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded inverse, whereas a lower semi-frame has an unbounded frame operator, with bounded inverse. For upper semi-frames, in the discrete and the continuous case, we build two natural Hilbert scales which may yield a novel characterization of certain function spaces of interest in signal processing. We present some examples and, in addition, some results concerning the du"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0506","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":"1203.0506","created_at":"2026-05-18T03:43:28.511483+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.0506v1","created_at":"2026-05-18T03:43:28.511483+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0506","created_at":"2026-05-18T03:43:28.511483+00:00"},{"alias_kind":"pith_short_12","alias_value":"QLYJXM4LRFNR","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QLYJXM4LRFNRASOJ","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QLYJXM4L","created_at":"2026-05-18T12:27:18.751474+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/QLYJXM4LRFNRASOJVO7DB5CSP7","json":"https://pith.science/pith/QLYJXM4LRFNRASOJVO7DB5CSP7.json","graph_json":"https://pith.science/api/pith-number/QLYJXM4LRFNRASOJVO7DB5CSP7/graph.json","events_json":"https://pith.science/api/pith-number/QLYJXM4LRFNRASOJVO7DB5CSP7/events.json","paper":"https://pith.science/paper/QLYJXM4L"},"agent_actions":{"view_html":"https://pith.science/pith/QLYJXM4LRFNRASOJVO7DB5CSP7","download_json":"https://pith.science/pith/QLYJXM4LRFNRASOJVO7DB5CSP7.json","view_paper":"https://pith.science/paper/QLYJXM4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.0506&json=true","fetch_graph":"https://pith.science/api/pith-number/QLYJXM4LRFNRASOJVO7DB5CSP7/graph.json","fetch_events":"https://pith.science/api/pith-number/QLYJXM4LRFNRASOJVO7DB5CSP7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QLYJXM4LRFNRASOJVO7DB5CSP7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QLYJXM4LRFNRASOJVO7DB5CSP7/action/storage_attestation","attest_author":"https://pith.science/pith/QLYJXM4LRFNRASOJVO7DB5CSP7/action/author_attestation","sign_citation":"https://pith.science/pith/QLYJXM4LRFNRASOJVO7DB5CSP7/action/citation_signature","submit_replication":"https://pith.science/pith/QLYJXM4LRFNRASOJVO7DB5CSP7/action/replication_record"}},"created_at":"2026-05-18T03:43:28.511483+00:00","updated_at":"2026-05-18T03:43:28.511483+00:00"}