{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FZQJV52FCLWVUQM7UFMN76AJQH","short_pith_number":"pith:FZQJV52F","schema_version":"1.0","canonical_sha256":"2e609af74512ed5a419fa158dff80981f2b6f0f6c3a7b5cf406062b2c651cb57","source":{"kind":"arxiv","id":"1204.1159","version":1},"attestation_state":"computed","paper":{"title":"Weighted Plancherel estimates and sharp spectral multipliers for the Grushin operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Sikora, Alessio Martini","submitted_at":"2012-04-05T09:27:49Z","abstract_excerpt":"We study the Grushin operators acting on $\\R^{d_1}_{x'}\\times \\R^{d_2}_{x\"}$ and defined by the formula \\[ L=-\\sum_{\\jone=1}^{d_1}\\partial_{x'_\\jone}^2 - (\\sum_{\\jone=1}^{d_1}|x'_\\jone|^2) \\sum_{\\jtwo=1}^{d_2}\\partial_{x\"_\\jtwo}^2. \\] We obtain weighted Plancherel estimates for the considered operators. As a consequence we prove $L^p$ spectral multiplier results and Bochner-Riesz summability for the Grushin operators. These multiplier results are sharp if $d_1 \\ge d_2$. We discuss also an interesting phenomenon for weighted Plancherel estimates for $d_1 <d_2$. The described spectral multiplier"},"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":"1204.1159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-05T09:27:49Z","cross_cats_sorted":[],"title_canon_sha256":"2027b0918e2a31ddb367025a34b589df4fd2d88c6e24fd7a71bf382f52eec3ba","abstract_canon_sha256":"bb9b0e3d178eb837a9115a6465ef9b8bea49f1bef197a232e269ab13c49281d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:53.837241Z","signature_b64":"H80XAFkBBHfvEBwqt2zT7BrZsHyWIALaYnnzvE0d2wIYnSrr3o49L/cXp8g7jio5mWRd4i0/DDPT4xoLYvkYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e609af74512ed5a419fa158dff80981f2b6f0f6c3a7b5cf406062b2c651cb57","last_reissued_at":"2026-05-18T03:30:53.836402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:53.836402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted Plancherel estimates and sharp spectral multipliers for the Grushin operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Sikora, Alessio Martini","submitted_at":"2012-04-05T09:27:49Z","abstract_excerpt":"We study the Grushin operators acting on $\\R^{d_1}_{x'}\\times \\R^{d_2}_{x\"}$ and defined by the formula \\[ L=-\\sum_{\\jone=1}^{d_1}\\partial_{x'_\\jone}^2 - (\\sum_{\\jone=1}^{d_1}|x'_\\jone|^2) \\sum_{\\jtwo=1}^{d_2}\\partial_{x\"_\\jtwo}^2. \\] We obtain weighted Plancherel estimates for the considered operators. As a consequence we prove $L^p$ spectral multiplier results and Bochner-Riesz summability for the Grushin operators. These multiplier results are sharp if $d_1 \\ge d_2$. We discuss also an interesting phenomenon for weighted Plancherel estimates for $d_1 <d_2$. The described spectral multiplier"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1159","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":"1204.1159","created_at":"2026-05-18T03:30:53.836546+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.1159v1","created_at":"2026-05-18T03:30:53.836546+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1159","created_at":"2026-05-18T03:30:53.836546+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZQJV52FCLWV","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZQJV52FCLWVUQM7","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZQJV52F","created_at":"2026-05-18T12:27:06.952714+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/FZQJV52FCLWVUQM7UFMN76AJQH","json":"https://pith.science/pith/FZQJV52FCLWVUQM7UFMN76AJQH.json","graph_json":"https://pith.science/api/pith-number/FZQJV52FCLWVUQM7UFMN76AJQH/graph.json","events_json":"https://pith.science/api/pith-number/FZQJV52FCLWVUQM7UFMN76AJQH/events.json","paper":"https://pith.science/paper/FZQJV52F"},"agent_actions":{"view_html":"https://pith.science/pith/FZQJV52FCLWVUQM7UFMN76AJQH","download_json":"https://pith.science/pith/FZQJV52FCLWVUQM7UFMN76AJQH.json","view_paper":"https://pith.science/paper/FZQJV52F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.1159&json=true","fetch_graph":"https://pith.science/api/pith-number/FZQJV52FCLWVUQM7UFMN76AJQH/graph.json","fetch_events":"https://pith.science/api/pith-number/FZQJV52FCLWVUQM7UFMN76AJQH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZQJV52FCLWVUQM7UFMN76AJQH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZQJV52FCLWVUQM7UFMN76AJQH/action/storage_attestation","attest_author":"https://pith.science/pith/FZQJV52FCLWVUQM7UFMN76AJQH/action/author_attestation","sign_citation":"https://pith.science/pith/FZQJV52FCLWVUQM7UFMN76AJQH/action/citation_signature","submit_replication":"https://pith.science/pith/FZQJV52FCLWVUQM7UFMN76AJQH/action/replication_record"}},"created_at":"2026-05-18T03:30:53.836546+00:00","updated_at":"2026-05-18T03:30:53.836546+00:00"}