{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XYMVBYLJ6BMLI3OP7PDLOCQEAO","short_pith_number":"pith:XYMVBYLJ","schema_version":"1.0","canonical_sha256":"be1950e169f058b46dcffbc6b70a0403bbe44e913744d41209f8b82a97ee3dc7","source":{"kind":"arxiv","id":"1708.02788","version":1},"attestation_state":"computed","paper":{"title":"Fractional powers of the parabolic Hermite operator. Regularity properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jos\\'e L. Torrea, Marta de Le\\'on-Contreras","submitted_at":"2017-08-09T11:26:38Z","abstract_excerpt":"Let $\\mathcal{L}= \\partial_t- \\Delta_x+|x|^2$. Consider its Poisson semigroup $e^{-y\\sqrt{\\mathcal{L}}}$. For $\\alpha >0$ define the Parabolic Hermite-Zygmund spaces\n  $$\n  \\Lambda^\\alpha_{\\mathcal{L}}=\\left\\{f: \\:f\\in L^\\infty(\\mathbb{R}^{n+1})\\:\\; {\\rm and} \\:\\; \\left\\|\\partial_y^k e^{-y\\sqrt{\\mathcal{L}}} f \\right\\|_{L^\\infty(\\mathbb{R}^{n+1})}\\leq C_k y^{-k+\\alpha},\\;\\: {\\rm with }\\, k=[\\alpha]+1, y>0. \\right\\},\n  $$\n  with the obvious norm. It is shown that these spaces have a pointwise description of H\\\"older type.\n  The fractional powers $\\mathcal{L}^{\\pm \\beta}$ are well defined in the"},"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":"1708.02788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-09T11:26:38Z","cross_cats_sorted":[],"title_canon_sha256":"ea881c07259af78c29a51e72b89370768e5e928e35afd9683bedd43280fdfbb4","abstract_canon_sha256":"48a1d7113c33978c76b39e8a42c8f789169d7a2b3c475b4ee0306d5ae3dbdb1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:19.521483Z","signature_b64":"hURqtF5xmsB2frq/nUgx/s4k8yfADphVNPcx01TO9qLHSPBBTQ1HxsoxPVNNQBpHhv/z6hN8Onb7+yRUZ+/vDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be1950e169f058b46dcffbc6b70a0403bbe44e913744d41209f8b82a97ee3dc7","last_reissued_at":"2026-05-18T00:38:19.520794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:19.520794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional powers of the parabolic Hermite operator. Regularity properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jos\\'e L. Torrea, Marta de Le\\'on-Contreras","submitted_at":"2017-08-09T11:26:38Z","abstract_excerpt":"Let $\\mathcal{L}= \\partial_t- \\Delta_x+|x|^2$. Consider its Poisson semigroup $e^{-y\\sqrt{\\mathcal{L}}}$. For $\\alpha >0$ define the Parabolic Hermite-Zygmund spaces\n  $$\n  \\Lambda^\\alpha_{\\mathcal{L}}=\\left\\{f: \\:f\\in L^\\infty(\\mathbb{R}^{n+1})\\:\\; {\\rm and} \\:\\; \\left\\|\\partial_y^k e^{-y\\sqrt{\\mathcal{L}}} f \\right\\|_{L^\\infty(\\mathbb{R}^{n+1})}\\leq C_k y^{-k+\\alpha},\\;\\: {\\rm with }\\, k=[\\alpha]+1, y>0. \\right\\},\n  $$\n  with the obvious norm. It is shown that these spaces have a pointwise description of H\\\"older type.\n  The fractional powers $\\mathcal{L}^{\\pm \\beta}$ are well defined in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02788","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":"1708.02788","created_at":"2026-05-18T00:38:19.520889+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.02788v1","created_at":"2026-05-18T00:38:19.520889+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02788","created_at":"2026-05-18T00:38:19.520889+00:00"},{"alias_kind":"pith_short_12","alias_value":"XYMVBYLJ6BML","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XYMVBYLJ6BMLI3OP","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XYMVBYLJ","created_at":"2026-05-18T12:31:56.362134+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/XYMVBYLJ6BMLI3OP7PDLOCQEAO","json":"https://pith.science/pith/XYMVBYLJ6BMLI3OP7PDLOCQEAO.json","graph_json":"https://pith.science/api/pith-number/XYMVBYLJ6BMLI3OP7PDLOCQEAO/graph.json","events_json":"https://pith.science/api/pith-number/XYMVBYLJ6BMLI3OP7PDLOCQEAO/events.json","paper":"https://pith.science/paper/XYMVBYLJ"},"agent_actions":{"view_html":"https://pith.science/pith/XYMVBYLJ6BMLI3OP7PDLOCQEAO","download_json":"https://pith.science/pith/XYMVBYLJ6BMLI3OP7PDLOCQEAO.json","view_paper":"https://pith.science/paper/XYMVBYLJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.02788&json=true","fetch_graph":"https://pith.science/api/pith-number/XYMVBYLJ6BMLI3OP7PDLOCQEAO/graph.json","fetch_events":"https://pith.science/api/pith-number/XYMVBYLJ6BMLI3OP7PDLOCQEAO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XYMVBYLJ6BMLI3OP7PDLOCQEAO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XYMVBYLJ6BMLI3OP7PDLOCQEAO/action/storage_attestation","attest_author":"https://pith.science/pith/XYMVBYLJ6BMLI3OP7PDLOCQEAO/action/author_attestation","sign_citation":"https://pith.science/pith/XYMVBYLJ6BMLI3OP7PDLOCQEAO/action/citation_signature","submit_replication":"https://pith.science/pith/XYMVBYLJ6BMLI3OP7PDLOCQEAO/action/replication_record"}},"created_at":"2026-05-18T00:38:19.520889+00:00","updated_at":"2026-05-18T00:38:19.520889+00:00"}