{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:FFOXON7HLYJXNQOB5IFOHVU32V","short_pith_number":"pith:FFOXON7H","schema_version":"1.0","canonical_sha256":"295d7737e75e1376c1c1ea0ae3d69bd54e7d985e6605ec8bddff796c4ef7e76a","source":{"kind":"arxiv","id":"1903.07094","version":1},"attestation_state":"computed","paper":{"title":"Representing systems of dilations and translations in symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pavel A. Terekhin, Sergey V. Astashkin","submitted_at":"2019-03-17T14:13:51Z","abstract_excerpt":"Let $X$ be an arbitrary separable symmetric space on $[0,1]$. By using a combination of the frame approach and the notion of the multiplicator space $\\mathscr{M}(X)$ of $X$ with respect to the tensor product, we investigate the problem when the sequence of dyadic dilations and translations of a function $f\\in X$ is a representing system in the space $X$. The main result reads that this holds whenever $\\int_0^1 f(t)\\,dt\\ne 0$ and $f\\in \\mathscr{M}(X)$. Moreover, the condition $f\\in\\mathscr{M}(X)$ turns out to be sharp in a certain sense. In particular, we prove that a decreasing nonnegative fun"},"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":"1903.07094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-17T14:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"ece054e534423cfdcfe827c7222269a27ff03036c13be152593112fb585c0172","abstract_canon_sha256":"b03727510cce393ed01dd38974cb5f12ecca09cf0bc47ccbfc84c13fe9a7f3cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:04.240342Z","signature_b64":"vbjhvD4Ds/LcUVYTCO4SzNpNfbs1WLDfkQZBpPtovE3iYT9Wb0wdviRnrlFwy69qVVE0/E6/xACMVXNzlHaHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"295d7737e75e1376c1c1ea0ae3d69bd54e7d985e6605ec8bddff796c4ef7e76a","last_reissued_at":"2026-05-17T23:51:04.239781Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:04.239781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representing systems of dilations and translations in symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pavel A. Terekhin, Sergey V. Astashkin","submitted_at":"2019-03-17T14:13:51Z","abstract_excerpt":"Let $X$ be an arbitrary separable symmetric space on $[0,1]$. By using a combination of the frame approach and the notion of the multiplicator space $\\mathscr{M}(X)$ of $X$ with respect to the tensor product, we investigate the problem when the sequence of dyadic dilations and translations of a function $f\\in X$ is a representing system in the space $X$. The main result reads that this holds whenever $\\int_0^1 f(t)\\,dt\\ne 0$ and $f\\in \\mathscr{M}(X)$. Moreover, the condition $f\\in\\mathscr{M}(X)$ turns out to be sharp in a certain sense. In particular, we prove that a decreasing nonnegative fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07094","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":"1903.07094","created_at":"2026-05-17T23:51:04.239901+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.07094v1","created_at":"2026-05-17T23:51:04.239901+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07094","created_at":"2026-05-17T23:51:04.239901+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFOXON7HLYJX","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFOXON7HLYJXNQOB","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFOXON7H","created_at":"2026-05-18T12:33:15.570797+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/FFOXON7HLYJXNQOB5IFOHVU32V","json":"https://pith.science/pith/FFOXON7HLYJXNQOB5IFOHVU32V.json","graph_json":"https://pith.science/api/pith-number/FFOXON7HLYJXNQOB5IFOHVU32V/graph.json","events_json":"https://pith.science/api/pith-number/FFOXON7HLYJXNQOB5IFOHVU32V/events.json","paper":"https://pith.science/paper/FFOXON7H"},"agent_actions":{"view_html":"https://pith.science/pith/FFOXON7HLYJXNQOB5IFOHVU32V","download_json":"https://pith.science/pith/FFOXON7HLYJXNQOB5IFOHVU32V.json","view_paper":"https://pith.science/paper/FFOXON7H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.07094&json=true","fetch_graph":"https://pith.science/api/pith-number/FFOXON7HLYJXNQOB5IFOHVU32V/graph.json","fetch_events":"https://pith.science/api/pith-number/FFOXON7HLYJXNQOB5IFOHVU32V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFOXON7HLYJXNQOB5IFOHVU32V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFOXON7HLYJXNQOB5IFOHVU32V/action/storage_attestation","attest_author":"https://pith.science/pith/FFOXON7HLYJXNQOB5IFOHVU32V/action/author_attestation","sign_citation":"https://pith.science/pith/FFOXON7HLYJXNQOB5IFOHVU32V/action/citation_signature","submit_replication":"https://pith.science/pith/FFOXON7HLYJXNQOB5IFOHVU32V/action/replication_record"}},"created_at":"2026-05-17T23:51:04.239901+00:00","updated_at":"2026-05-17T23:51:04.239901+00:00"}