{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XEJB6NY2MTVSIVD757ZV6H43AM","short_pith_number":"pith:XEJB6NY2","schema_version":"1.0","canonical_sha256":"b9121f371a64eb24547feff35f1f9b0321f5bb9d65f981fca2a6ec679d4c2403","source":{"kind":"arxiv","id":"1707.03603","version":4},"attestation_state":"computed","paper":{"title":"Integral representation of solutions to higher-order fractional Dirichlet problems on balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Salda\\~na, Nicola Abatangelo, Sven Jarohs","submitted_at":"2017-07-12T09:02:27Z","abstract_excerpt":"We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power $s>0$ of the Laplacian. We are able to prescribe values outside the domain and boundary data of different orders using explicit Poisson-type kernels and a new notion of higher-order boundary operator, which recovers normal derivatives if $s$ is a natural number. Our results unify and generalize previous approaches in the study of polyharmonic operators and fractional Laplacians. As applications, we show a novel characterization of $s$-harmonic functions in terms of Marti"},"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":"1707.03603","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-12T09:02:27Z","cross_cats_sorted":[],"title_canon_sha256":"d5c34c714cbe6cf94d40b038f924a4eea586cde929774cf59ac264f718dc0d6a","abstract_canon_sha256":"8335132f5a2c3d821cb13c3530641b1f5bed301211eca9869100541861bc074e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:34.415398Z","signature_b64":"CCD4Hd9YGUJ/YbAKwjBwnDqLOXvyHsGyUZO8iVYRGFDFBEju1xZXDXDT/7jBeQx1/0ArugpDstWg6AgyjrD+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9121f371a64eb24547feff35f1f9b0321f5bb9d65f981fca2a6ec679d4c2403","last_reissued_at":"2026-05-18T00:05:34.414888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:34.414888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral representation of solutions to higher-order fractional Dirichlet problems on balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Salda\\~na, Nicola Abatangelo, Sven Jarohs","submitted_at":"2017-07-12T09:02:27Z","abstract_excerpt":"We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power $s>0$ of the Laplacian. We are able to prescribe values outside the domain and boundary data of different orders using explicit Poisson-type kernels and a new notion of higher-order boundary operator, which recovers normal derivatives if $s$ is a natural number. Our results unify and generalize previous approaches in the study of polyharmonic operators and fractional Laplacians. As applications, we show a novel characterization of $s$-harmonic functions in terms of Marti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03603","kind":"arxiv","version":4},"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":"1707.03603","created_at":"2026-05-18T00:05:34.414969+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.03603v4","created_at":"2026-05-18T00:05:34.414969+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03603","created_at":"2026-05-18T00:05:34.414969+00:00"},{"alias_kind":"pith_short_12","alias_value":"XEJB6NY2MTVS","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"XEJB6NY2MTVSIVD7","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"XEJB6NY2","created_at":"2026-05-18T12:31:53.515858+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/XEJB6NY2MTVSIVD757ZV6H43AM","json":"https://pith.science/pith/XEJB6NY2MTVSIVD757ZV6H43AM.json","graph_json":"https://pith.science/api/pith-number/XEJB6NY2MTVSIVD757ZV6H43AM/graph.json","events_json":"https://pith.science/api/pith-number/XEJB6NY2MTVSIVD757ZV6H43AM/events.json","paper":"https://pith.science/paper/XEJB6NY2"},"agent_actions":{"view_html":"https://pith.science/pith/XEJB6NY2MTVSIVD757ZV6H43AM","download_json":"https://pith.science/pith/XEJB6NY2MTVSIVD757ZV6H43AM.json","view_paper":"https://pith.science/paper/XEJB6NY2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.03603&json=true","fetch_graph":"https://pith.science/api/pith-number/XEJB6NY2MTVSIVD757ZV6H43AM/graph.json","fetch_events":"https://pith.science/api/pith-number/XEJB6NY2MTVSIVD757ZV6H43AM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XEJB6NY2MTVSIVD757ZV6H43AM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XEJB6NY2MTVSIVD757ZV6H43AM/action/storage_attestation","attest_author":"https://pith.science/pith/XEJB6NY2MTVSIVD757ZV6H43AM/action/author_attestation","sign_citation":"https://pith.science/pith/XEJB6NY2MTVSIVD757ZV6H43AM/action/citation_signature","submit_replication":"https://pith.science/pith/XEJB6NY2MTVSIVD757ZV6H43AM/action/replication_record"}},"created_at":"2026-05-18T00:05:34.414969+00:00","updated_at":"2026-05-18T00:05:34.414969+00:00"}