{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZBOJZOSVBCQBRT2BNUEDIQNMMU","short_pith_number":"pith:ZBOJZOSV","schema_version":"1.0","canonical_sha256":"c85c9cba5508a018cf416d083441ac6504d2df4530d025ea3e871e0f5ec7684a","source":{"kind":"arxiv","id":"1506.06499","version":1},"attestation_state":"computed","paper":{"title":"Weighted Bergman-Dirichlet and Bargmann-Dirichlet spaces of order $m$ in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ahmed Intissar, Allal Ghanmi, Ayman El Fardi, Mohammed Ziyat","submitted_at":"2015-06-22T08:24:34Z","abstract_excerpt":"We introduce and study a generalization of the classical weighted Bergman and Dirichlet spaces on the unit ball in high dimension, the Bergman-Dirichlet spaces. Their counterparts on the whole $n$-complex space, the Bargmann-Dirichlet spaces, are also introduced and studied. Mainly, we give a complete description of the considered spaces, including orthonormal basis and the explicit formulas for their reproducing kernel functions. Moreover, we investigate their asymptotic behavior when the curvature goes to $0$."},"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":"1506.06499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-22T08:24:34Z","cross_cats_sorted":[],"title_canon_sha256":"1de2591332714db487501e595e2d382bee140c5214c1884f7610f039761a7245","abstract_canon_sha256":"39c6e4f0cdeb3b56fc41fbbb07098ce69f472d84413600ee4d0d607ebd21caa7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:45.045534Z","signature_b64":"Q7aBeL02h9GiNLaoUkrxZMyMT+AyZCvCSG67LiLXv5p8NbFsZDFqtH2bwIlOX6aUE2Ki2SYgGBzTikB1FRKiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c85c9cba5508a018cf416d083441ac6504d2df4530d025ea3e871e0f5ec7684a","last_reissued_at":"2026-05-18T01:41:45.044870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:45.044870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted Bergman-Dirichlet and Bargmann-Dirichlet spaces of order $m$ in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ahmed Intissar, Allal Ghanmi, Ayman El Fardi, Mohammed Ziyat","submitted_at":"2015-06-22T08:24:34Z","abstract_excerpt":"We introduce and study a generalization of the classical weighted Bergman and Dirichlet spaces on the unit ball in high dimension, the Bergman-Dirichlet spaces. Their counterparts on the whole $n$-complex space, the Bargmann-Dirichlet spaces, are also introduced and studied. Mainly, we give a complete description of the considered spaces, including orthonormal basis and the explicit formulas for their reproducing kernel functions. Moreover, we investigate their asymptotic behavior when the curvature goes to $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06499","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":"1506.06499","created_at":"2026-05-18T01:41:45.044960+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.06499v1","created_at":"2026-05-18T01:41:45.044960+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06499","created_at":"2026-05-18T01:41:45.044960+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZBOJZOSVBCQB","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZBOJZOSVBCQBRT2B","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZBOJZOSV","created_at":"2026-05-18T12:29:52.810259+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/ZBOJZOSVBCQBRT2BNUEDIQNMMU","json":"https://pith.science/pith/ZBOJZOSVBCQBRT2BNUEDIQNMMU.json","graph_json":"https://pith.science/api/pith-number/ZBOJZOSVBCQBRT2BNUEDIQNMMU/graph.json","events_json":"https://pith.science/api/pith-number/ZBOJZOSVBCQBRT2BNUEDIQNMMU/events.json","paper":"https://pith.science/paper/ZBOJZOSV"},"agent_actions":{"view_html":"https://pith.science/pith/ZBOJZOSVBCQBRT2BNUEDIQNMMU","download_json":"https://pith.science/pith/ZBOJZOSVBCQBRT2BNUEDIQNMMU.json","view_paper":"https://pith.science/paper/ZBOJZOSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.06499&json=true","fetch_graph":"https://pith.science/api/pith-number/ZBOJZOSVBCQBRT2BNUEDIQNMMU/graph.json","fetch_events":"https://pith.science/api/pith-number/ZBOJZOSVBCQBRT2BNUEDIQNMMU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZBOJZOSVBCQBRT2BNUEDIQNMMU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZBOJZOSVBCQBRT2BNUEDIQNMMU/action/storage_attestation","attest_author":"https://pith.science/pith/ZBOJZOSVBCQBRT2BNUEDIQNMMU/action/author_attestation","sign_citation":"https://pith.science/pith/ZBOJZOSVBCQBRT2BNUEDIQNMMU/action/citation_signature","submit_replication":"https://pith.science/pith/ZBOJZOSVBCQBRT2BNUEDIQNMMU/action/replication_record"}},"created_at":"2026-05-18T01:41:45.044960+00:00","updated_at":"2026-05-18T01:41:45.044960+00:00"}