{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:Y4ZQW6F7NWQIT6WVF3GISFP5MQ","short_pith_number":"pith:Y4ZQW6F7","schema_version":"1.0","canonical_sha256":"c7330b78bf6da089fad52ecc8915fd642eb37be5a97c3b58c63634bf2e0487d7","source":{"kind":"arxiv","id":"1610.00268","version":2},"attestation_state":"computed","paper":{"title":"Balayage for Riesz kernels with application to potential theory for the associated Green kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Bent Fuglede, Natalia Zorii","submitted_at":"2016-10-02T12:19:24Z","abstract_excerpt":"We study properties of the $\\alpha$-Green kernel $g_D^\\alpha$ of order $0<\\alpha\\leqslant2$ for a domain $D\\subset\\mathbb R^n$, $n\\geqslant3$. This kernel is associated with the $\\alpha$-Riesz kernel $|x-y|^{\\alpha-n}$, $x,y\\in\\mathbb R^n$, in a manner particularly well known in the case $\\alpha=2$. Besides the usual principles of potential theory, we establish for the $\\alpha$-Green kernel the property of consistency. This allows us to prove the completeness of the cone of positive measures $\\mu$ on $D$ with finite energy $g_D^\\alpha(\\mu,\\mu):=\\iint g_D^\\alpha(x,y)\\,d\\mu(x)\\,d\\mu(y)$ in the t"},"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":"1610.00268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-02T12:19:24Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"3a14445bd8510d3406d8ce16524744ef3aea096bb067fb09f520c2f3a84b7152","abstract_canon_sha256":"42f5f742f691eedbe4e218c322406e0078b994059c33d1ff8a6f690859cbf2fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:24.581918Z","signature_b64":"KsbSIebMGl+Ykx/vBmD9kCp29XTLKzxkt/plsRrUb7KBxXz8eaOUIma1bc4bPXuIMBNQa9QJ/LKO8CCj97VxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7330b78bf6da089fad52ecc8915fd642eb37be5a97c3b58c63634bf2e0487d7","last_reissued_at":"2026-05-18T00:36:24.581183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:24.581183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Balayage for Riesz kernels with application to potential theory for the associated Green kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Bent Fuglede, Natalia Zorii","submitted_at":"2016-10-02T12:19:24Z","abstract_excerpt":"We study properties of the $\\alpha$-Green kernel $g_D^\\alpha$ of order $0<\\alpha\\leqslant2$ for a domain $D\\subset\\mathbb R^n$, $n\\geqslant3$. This kernel is associated with the $\\alpha$-Riesz kernel $|x-y|^{\\alpha-n}$, $x,y\\in\\mathbb R^n$, in a manner particularly well known in the case $\\alpha=2$. Besides the usual principles of potential theory, we establish for the $\\alpha$-Green kernel the property of consistency. This allows us to prove the completeness of the cone of positive measures $\\mu$ on $D$ with finite energy $g_D^\\alpha(\\mu,\\mu):=\\iint g_D^\\alpha(x,y)\\,d\\mu(x)\\,d\\mu(y)$ in the t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00268","kind":"arxiv","version":2},"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":"1610.00268","created_at":"2026-05-18T00:36:24.581295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00268v2","created_at":"2026-05-18T00:36:24.581295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00268","created_at":"2026-05-18T00:36:24.581295+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y4ZQW6F7NWQI","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y4ZQW6F7NWQIT6WV","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y4ZQW6F7","created_at":"2026-05-18T12:30:53.716459+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/Y4ZQW6F7NWQIT6WVF3GISFP5MQ","json":"https://pith.science/pith/Y4ZQW6F7NWQIT6WVF3GISFP5MQ.json","graph_json":"https://pith.science/api/pith-number/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/graph.json","events_json":"https://pith.science/api/pith-number/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/events.json","paper":"https://pith.science/paper/Y4ZQW6F7"},"agent_actions":{"view_html":"https://pith.science/pith/Y4ZQW6F7NWQIT6WVF3GISFP5MQ","download_json":"https://pith.science/pith/Y4ZQW6F7NWQIT6WVF3GISFP5MQ.json","view_paper":"https://pith.science/paper/Y4ZQW6F7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00268&json=true","fetch_graph":"https://pith.science/api/pith-number/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/graph.json","fetch_events":"https://pith.science/api/pith-number/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/action/storage_attestation","attest_author":"https://pith.science/pith/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/action/author_attestation","sign_citation":"https://pith.science/pith/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/action/citation_signature","submit_replication":"https://pith.science/pith/Y4ZQW6F7NWQIT6WVF3GISFP5MQ/action/replication_record"}},"created_at":"2026-05-18T00:36:24.581295+00:00","updated_at":"2026-05-18T00:36:24.581295+00:00"}