{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:VS4FKZJ4VBY34X5Q5W4DPRUDXB","short_pith_number":"pith:VS4FKZJ4","schema_version":"1.0","canonical_sha256":"acb855653ca871be5fb0edb837c683b849160c9bc28f40e7c7a5b0f64bd9bb11","source":{"kind":"arxiv","id":"1006.0415","version":2},"attestation_state":"computed","paper":{"title":"Affine fractals as boundaries and their harmonic analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dorin Ervin Dutkay, Palle E.T. Jorgensen","submitted_at":"2010-06-02T15:00:40Z","abstract_excerpt":"We introduce the notion of boundary representation for fractal Fourier expansions, starting with a familiar notion of spectral pairs for affine fractal measures. Specializing to one dimension, we establish boundary representations for these fractals. We prove that as sets these fractals arise as boundaries of functions in closed subspaces of the Hardy space $H^2$. By this we mean that there are lacunary subsets $\\Gamma$ of the non-negative integers, and associated closed $\\Gamma$-subspace in the Hardy space $H^2(\\bd)$, $\\bd$ denoting the disk, such that for every function $f$ in in $H^2(\\Gamma"},"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":"1006.0415","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-06-02T15:00:40Z","cross_cats_sorted":[],"title_canon_sha256":"96e9576e2835400a198980028f0139ccb124c00b696544f6d761492a77ddf715","abstract_canon_sha256":"f7d2ba319c677f8c9b757e151e67144d886a22ebcc83bbb12768f67379559161"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:55.750693Z","signature_b64":"Z1AgEK/XP7AoZYeUi+Ff3zvAohA6H2pRzppfyTbqF+5Dl1juCiI44Ly89hJSJpYeyZxljNCUQ4WIBt+zAN/gBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acb855653ca871be5fb0edb837c683b849160c9bc28f40e7c7a5b0f64bd9bb11","last_reissued_at":"2026-05-18T04:41:55.750116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:55.750116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine fractals as boundaries and their harmonic analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dorin Ervin Dutkay, Palle E.T. Jorgensen","submitted_at":"2010-06-02T15:00:40Z","abstract_excerpt":"We introduce the notion of boundary representation for fractal Fourier expansions, starting with a familiar notion of spectral pairs for affine fractal measures. Specializing to one dimension, we establish boundary representations for these fractals. We prove that as sets these fractals arise as boundaries of functions in closed subspaces of the Hardy space $H^2$. By this we mean that there are lacunary subsets $\\Gamma$ of the non-negative integers, and associated closed $\\Gamma$-subspace in the Hardy space $H^2(\\bd)$, $\\bd$ denoting the disk, such that for every function $f$ in in $H^2(\\Gamma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0415","kind":"arxiv","version":2},"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":"1006.0415","created_at":"2026-05-18T04:41:55.750210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.0415v2","created_at":"2026-05-18T04:41:55.750210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0415","created_at":"2026-05-18T04:41:55.750210+00:00"},{"alias_kind":"pith_short_12","alias_value":"VS4FKZJ4VBY3","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"VS4FKZJ4VBY34X5Q","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"VS4FKZJ4","created_at":"2026-05-18T12:26:15.391820+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/VS4FKZJ4VBY34X5Q5W4DPRUDXB","json":"https://pith.science/pith/VS4FKZJ4VBY34X5Q5W4DPRUDXB.json","graph_json":"https://pith.science/api/pith-number/VS4FKZJ4VBY34X5Q5W4DPRUDXB/graph.json","events_json":"https://pith.science/api/pith-number/VS4FKZJ4VBY34X5Q5W4DPRUDXB/events.json","paper":"https://pith.science/paper/VS4FKZJ4"},"agent_actions":{"view_html":"https://pith.science/pith/VS4FKZJ4VBY34X5Q5W4DPRUDXB","download_json":"https://pith.science/pith/VS4FKZJ4VBY34X5Q5W4DPRUDXB.json","view_paper":"https://pith.science/paper/VS4FKZJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.0415&json=true","fetch_graph":"https://pith.science/api/pith-number/VS4FKZJ4VBY34X5Q5W4DPRUDXB/graph.json","fetch_events":"https://pith.science/api/pith-number/VS4FKZJ4VBY34X5Q5W4DPRUDXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VS4FKZJ4VBY34X5Q5W4DPRUDXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VS4FKZJ4VBY34X5Q5W4DPRUDXB/action/storage_attestation","attest_author":"https://pith.science/pith/VS4FKZJ4VBY34X5Q5W4DPRUDXB/action/author_attestation","sign_citation":"https://pith.science/pith/VS4FKZJ4VBY34X5Q5W4DPRUDXB/action/citation_signature","submit_replication":"https://pith.science/pith/VS4FKZJ4VBY34X5Q5W4DPRUDXB/action/replication_record"}},"created_at":"2026-05-18T04:41:55.750210+00:00","updated_at":"2026-05-18T04:41:55.750210+00:00"}