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Let $f_0\\in C^\\infty_0(\\mathbb{R})$ be a smooth cutoff equal 1 near zero. We firstly show that the high frequency part $(1-f_0)(P)e^{-it\\Lambda_g^\\sigma}$ satisfies global in time Strichartz estimates as on $\\mathbb{R}^d$ of dimension $d\\geq 2$ inside a compact set under non-"},"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":"1705.04403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-11T23:45:07Z","cross_cats_sorted":[],"title_canon_sha256":"5cd2232ab0c000c376b9f3ec92060b5e739164273f19021fd3efc1ffade4e9ab","abstract_canon_sha256":"6ff69fafafe58eb0f6644a44fce879b67b0a25e4d474cf9b368af78d5ad000fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:19.441917Z","signature_b64":"wFoSUyy2W6pARzzgX2RcGVwvMXZWDpk7RXNnTltr7fzHuFVUSeD17WqG8fA7sk0HlG/6bLFMlfDc8NRtQUVSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fe92831442492b1b116461ad6bb36cfc3aa0654280b8b417088ad7d41160b6c","last_reissued_at":"2026-05-18T00:10:19.441303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:19.441303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global in time Strichartz estimates for the fractional Schr\\\"odinger equations on asymptotically Euclidean manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2017-05-11T23:45:07Z","abstract_excerpt":"In this paper, we prove global in time Strichartz estimates for the fractional Schr\\\"odinger operators, namely $e^{-it\\Lambda_g^\\sigma}$ with $\\sigma \\in (0,\\infty)\\backslash \\{1\\}$ and $\\Lambda_g:=\\sqrt{-\\Delta_g}$ where $\\Delta_g$ is the Laplace-Beltrami operator on asymptotically Euclidean manifolds $(\\mathbb{R}^d,g)$. Let $f_0\\in C^\\infty_0(\\mathbb{R})$ be a smooth cutoff equal 1 near zero. We firstly show that the high frequency part $(1-f_0)(P)e^{-it\\Lambda_g^\\sigma}$ satisfies global in time Strichartz estimates as on $\\mathbb{R}^d$ of dimension $d\\geq 2$ inside a compact set under non-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04403","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":"1705.04403","created_at":"2026-05-18T00:10:19.441428+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.04403v2","created_at":"2026-05-18T00:10:19.441428+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04403","created_at":"2026-05-18T00:10:19.441428+00:00"},{"alias_kind":"pith_short_12","alias_value":"D7USQMKEESJL","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"D7USQMKEESJLDMIW","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"D7USQMKE","created_at":"2026-05-18T12:31:10.602751+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/D7USQMKEESJLDMIWIYNNNOZWZ7","json":"https://pith.science/pith/D7USQMKEESJLDMIWIYNNNOZWZ7.json","graph_json":"https://pith.science/api/pith-number/D7USQMKEESJLDMIWIYNNNOZWZ7/graph.json","events_json":"https://pith.science/api/pith-number/D7USQMKEESJLDMIWIYNNNOZWZ7/events.json","paper":"https://pith.science/paper/D7USQMKE"},"agent_actions":{"view_html":"https://pith.science/pith/D7USQMKEESJLDMIWIYNNNOZWZ7","download_json":"https://pith.science/pith/D7USQMKEESJLDMIWIYNNNOZWZ7.json","view_paper":"https://pith.science/paper/D7USQMKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.04403&json=true","fetch_graph":"https://pith.science/api/pith-number/D7USQMKEESJLDMIWIYNNNOZWZ7/graph.json","fetch_events":"https://pith.science/api/pith-number/D7USQMKEESJLDMIWIYNNNOZWZ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D7USQMKEESJLDMIWIYNNNOZWZ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D7USQMKEESJLDMIWIYNNNOZWZ7/action/storage_attestation","attest_author":"https://pith.science/pith/D7USQMKEESJLDMIWIYNNNOZWZ7/action/author_attestation","sign_citation":"https://pith.science/pith/D7USQMKEESJLDMIWIYNNNOZWZ7/action/citation_signature","submit_replication":"https://pith.science/pith/D7USQMKEESJLDMIWIYNNNOZWZ7/action/replication_record"}},"created_at":"2026-05-18T00:10:19.441428+00:00","updated_at":"2026-05-18T00:10:19.441428+00:00"}