{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BNVEKUSEACCLKZOYAJ5Z7LBCCJ","short_pith_number":"pith:BNVEKUSE","schema_version":"1.0","canonical_sha256":"0b6a4552440084b565d8027b9fac221249408dc6992ffbcfcca49da31b0ad103","source":{"kind":"arxiv","id":"1903.04397","version":1},"attestation_state":"computed","paper":{"title":"Wavelet Series Representation and Geometric Properties of Harmonizable Fractional Stable Sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao","submitted_at":"2019-03-11T16:09:22Z","abstract_excerpt":"Let $Z^H= \\{Z^H(t), t \\in \\R^N\\}$ be a real-valued $N$-parameter harmonizable fractional stable sheet with index $H = (H_1, \\ldots, H_N) \\in (0, 1)^N$. We establish a random wavelet series expansion for $Z^H$ which is almost surely convergent in all the H\\\"older spaces $C^\\gamma ([-M,M]^N)$, where $M>0$ and $\\gamma\\in (0, \\min\\{H_1,\\ldots, H_N\\})$ are arbitrary. One of the main ingredients for proving the latter result is the LePage representation for a rotationally invariant stable random measure.\n  Also, let $X=\\{X(t), t \\in \\R^N\\}$ be an $\\R^d$-valued harmonizable fractional stable sheet wh"},"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":"1903.04397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-11T16:09:22Z","cross_cats_sorted":[],"title_canon_sha256":"b35e8ec439805ee9e2c3697b14ad535e5f7bad86d0ed8607ffa4a7430521d23c","abstract_canon_sha256":"0b44fa005e0a0947130b5b2defa3eefd58c124dc29b5434b7559446fd52e80bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:35.474798Z","signature_b64":"KSg6wt7lu+06n0spi2jmAPlewkXgmEuLGgXh0vHzuBmA6W2yao+/2phFxvN2KNfNlnbedrVpkONbG/bbyIdKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b6a4552440084b565d8027b9fac221249408dc6992ffbcfcca49da31b0ad103","last_reissued_at":"2026-05-17T23:51:35.474024Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:35.474024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wavelet Series Representation and Geometric Properties of Harmonizable Fractional Stable Sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao","submitted_at":"2019-03-11T16:09:22Z","abstract_excerpt":"Let $Z^H= \\{Z^H(t), t \\in \\R^N\\}$ be a real-valued $N$-parameter harmonizable fractional stable sheet with index $H = (H_1, \\ldots, H_N) \\in (0, 1)^N$. We establish a random wavelet series expansion for $Z^H$ which is almost surely convergent in all the H\\\"older spaces $C^\\gamma ([-M,M]^N)$, where $M>0$ and $\\gamma\\in (0, \\min\\{H_1,\\ldots, H_N\\})$ are arbitrary. One of the main ingredients for proving the latter result is the LePage representation for a rotationally invariant stable random measure.\n  Also, let $X=\\{X(t), t \\in \\R^N\\}$ be an $\\R^d$-valued harmonizable fractional stable sheet wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04397","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":"1903.04397","created_at":"2026-05-17T23:51:35.474164+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.04397v1","created_at":"2026-05-17T23:51:35.474164+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04397","created_at":"2026-05-17T23:51:35.474164+00:00"},{"alias_kind":"pith_short_12","alias_value":"BNVEKUSEACCL","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BNVEKUSEACCLKZOY","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BNVEKUSE","created_at":"2026-05-18T12:33:12.712433+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/BNVEKUSEACCLKZOYAJ5Z7LBCCJ","json":"https://pith.science/pith/BNVEKUSEACCLKZOYAJ5Z7LBCCJ.json","graph_json":"https://pith.science/api/pith-number/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/graph.json","events_json":"https://pith.science/api/pith-number/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/events.json","paper":"https://pith.science/paper/BNVEKUSE"},"agent_actions":{"view_html":"https://pith.science/pith/BNVEKUSEACCLKZOYAJ5Z7LBCCJ","download_json":"https://pith.science/pith/BNVEKUSEACCLKZOYAJ5Z7LBCCJ.json","view_paper":"https://pith.science/paper/BNVEKUSE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.04397&json=true","fetch_graph":"https://pith.science/api/pith-number/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/action/storage_attestation","attest_author":"https://pith.science/pith/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/action/author_attestation","sign_citation":"https://pith.science/pith/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/action/citation_signature","submit_replication":"https://pith.science/pith/BNVEKUSEACCLKZOYAJ5Z7LBCCJ/action/replication_record"}},"created_at":"2026-05-17T23:51:35.474164+00:00","updated_at":"2026-05-17T23:51:35.474164+00:00"}