{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2W4A42IXZJQD3U3HZLCWPU2BYF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2551fc18b5f0d59d595e8a8519cd3a4fa5aea0c0179939484e25758d682b40cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-23T13:13:11Z","title_canon_sha256":"471bca01e9c56a90e550650abeb1f548327895a6e19ebf2b114d8d466ccd61c0"},"schema_version":"1.0","source":{"id":"1802.08518","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08518","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08518v3","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08518","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"2W4A42IXZJQD","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2W4A42IXZJQD3U3H","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2W4A42IX","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:1f8074a5a065d0ad79bc1a240f41b9c5caa7a33ee629e9ed2f63e9fcd6375e34","target":"graph","created_at":"2026-05-17T23:46:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\Delta$ and $L=\\Delta -\\|\\mathbf x\\|^2$ be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space $\\mathcal H^1$ associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with respect to the semigroup $e^{tL}$. We prove that the space $\\mathcal H^1$ admits characterizations by relevant Riesz transforms and atomic decompositions. The atoms which occur in the atomic decompositions are of local type.","authors_text":"Agnieszka Hejna","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-23T13:13:11Z","title":"Hardy spaces for the Dunkl harmonic oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08518","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0c4115828e20ba03d2b3a9039ba466135d291f1da979d09a5631217af145f494","target":"record","created_at":"2026-05-17T23:46:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2551fc18b5f0d59d595e8a8519cd3a4fa5aea0c0179939484e25758d682b40cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-23T13:13:11Z","title_canon_sha256":"471bca01e9c56a90e550650abeb1f548327895a6e19ebf2b114d8d466ccd61c0"},"schema_version":"1.0","source":{"id":"1802.08518","kind":"arxiv","version":3}},"canonical_sha256":"d5b80e6917ca603dd367cac567d341c16a20a8d183dd7f364e1f877aa178e862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5b80e6917ca603dd367cac567d341c16a20a8d183dd7f364e1f877aa178e862","first_computed_at":"2026-05-17T23:46:30.770142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:30.770142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1MGbudLGhZWfRxAGMZdLSnSJFbfADmTkEjqfOy/+ev7P+l2oqcosTFTN1ZiaMq9FycZkiVePIcKMF6yzZ7d6Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:30.770874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08518","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c4115828e20ba03d2b3a9039ba466135d291f1da979d09a5631217af145f494","sha256:1f8074a5a065d0ad79bc1a240f41b9c5caa7a33ee629e9ed2f63e9fcd6375e34"],"state_sha256":"f6c12ebe2b523281957782dc5a993a60ccc6920b7e750ea98bcc84ec9005fa61"}