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We suppose that the cut-off resolvent $R_\\chi(\\theta)=\\chi(\\mathcal U(T, 0)-e^{-i\\theta})^{-1}\\chi$, where $\\mathcal U(T, 0)$ is the monodromy operator and $T$ the period of $a(t,x)$, admits an holomorphic continuation to $\\{\\theta\\in\\mathbb{C}\\ :\\ \\textrm{Im}(\\theta) \\geq 0\\}$, for $n \\geq 3$ , odd, and to $\\{ \\thet"},"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":"1102.4268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T16:11:39Z","cross_cats_sorted":[],"title_canon_sha256":"400e7dcacb17d2f0be9598cdc72dade0393a21ffdc8b5fa721b104e743f8d6c8","abstract_canon_sha256":"179c1de2372d30f3bc204294bcf598e277c9c4a5a72b6bfeaabc9b597d5707b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:10.556124Z","signature_b64":"7x185zMBK9ZbhW/xnM64l1wuFbRCDVIuuA5VTEqlVzZX46A4pWX4TBtx/8rDMj9H+OsQcmi9U5/3NV2LAb5rAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d39bf2a3c40ca9eca2a00edd48f8a5e5ab573b613e1761a36973099d4a6620c","last_reissued_at":"2026-05-18T04:28:10.555578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:10.555578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local energy decay in even dimensions for the wave equation with a time-periodic non-trapping metric and applications to Strichartz estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yavar Kian","submitted_at":"2011-02-21T16:11:39Z","abstract_excerpt":"We obtain local energy decay as well as global Strichartz estimates for the solutions $u$ of the wave equation $\\partial_t^2 u-div_x(a(t,x)\\nabla_xu)=0,\\ t\\in{\\R},\\ x\\in{\\R}^n,$ with time-periodic non-trapping metric $a(t,x)$ equal to $1$ outside a compact set with respect to $x$. We suppose that the cut-off resolvent $R_\\chi(\\theta)=\\chi(\\mathcal U(T, 0)-e^{-i\\theta})^{-1}\\chi$, where $\\mathcal U(T, 0)$ is the monodromy operator and $T$ the period of $a(t,x)$, admits an holomorphic continuation to $\\{\\theta\\in\\mathbb{C}\\ :\\ \\textrm{Im}(\\theta) \\geq 0\\}$, for $n \\geq 3$ , odd, and to $\\{ \\thet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4268","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":"1102.4268","created_at":"2026-05-18T04:28:10.555661+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.4268v1","created_at":"2026-05-18T04:28:10.555661+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4268","created_at":"2026-05-18T04:28:10.555661+00:00"},{"alias_kind":"pith_short_12","alias_value":"HU436KR4IDFJ","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HU436KR4IDFJ5SRK","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HU436KR4","created_at":"2026-05-18T12:26:30.835961+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/HU436KR4IDFJ5SRKADW5JD4KLZ","json":"https://pith.science/pith/HU436KR4IDFJ5SRKADW5JD4KLZ.json","graph_json":"https://pith.science/api/pith-number/HU436KR4IDFJ5SRKADW5JD4KLZ/graph.json","events_json":"https://pith.science/api/pith-number/HU436KR4IDFJ5SRKADW5JD4KLZ/events.json","paper":"https://pith.science/paper/HU436KR4"},"agent_actions":{"view_html":"https://pith.science/pith/HU436KR4IDFJ5SRKADW5JD4KLZ","download_json":"https://pith.science/pith/HU436KR4IDFJ5SRKADW5JD4KLZ.json","view_paper":"https://pith.science/paper/HU436KR4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.4268&json=true","fetch_graph":"https://pith.science/api/pith-number/HU436KR4IDFJ5SRKADW5JD4KLZ/graph.json","fetch_events":"https://pith.science/api/pith-number/HU436KR4IDFJ5SRKADW5JD4KLZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HU436KR4IDFJ5SRKADW5JD4KLZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HU436KR4IDFJ5SRKADW5JD4KLZ/action/storage_attestation","attest_author":"https://pith.science/pith/HU436KR4IDFJ5SRKADW5JD4KLZ/action/author_attestation","sign_citation":"https://pith.science/pith/HU436KR4IDFJ5SRKADW5JD4KLZ/action/citation_signature","submit_replication":"https://pith.science/pith/HU436KR4IDFJ5SRKADW5JD4KLZ/action/replication_record"}},"created_at":"2026-05-18T04:28:10.555661+00:00","updated_at":"2026-05-18T04:28:10.555661+00:00"}