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Let $ U(t,0)$ be the associated propagator and let $R(\\theta)=e^{-D<x>}(U(T,0)-e^{-i\\theta})^{-1}e^{-D<x>}$ be the resolvent of the Floquet operator $U(T,0)$ defined for $\\im(\\theta)>BT $ with $B>0$ sufficiently large. We establish a meromorphic continuation of $R(\\theta)$ from which we deduce the asymptotic expansion of $e^{-(D+\\epsilon)<x>}U(t,0)e^{-D<x>}f$, where $f\\in \\dot{H}^1(\\R^n)\\times L^2(\\R^n)$, as $t\\to+\\infty$ with a "},"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":"1103.2530","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-13T17:11:09Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"59d493fea006deae91a71f075d8313bf5450ae920218e105cf23aa4fa4b0bea1","abstract_canon_sha256":"755480302aceebd139a75a27e8b0447166ad682a5fc5d8996ce0cebd8e50314d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:22.532369Z","signature_b64":"kkju029UoHbbH7P51YiLF9vVP8jYmOGOLPBznNcGu1sbU2d3mmk80rSoPG1/mxanqb3/Qf6WyzAx+wnTSbH7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45f457900d279b77f6ef0ec18d85ad6a9a3c439b1b275e952dbc0a3b8b2aa71f","last_reissued_at":"2026-05-18T04:16:22.531846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:22.531846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the meromorphic continuation of the resolvent for the wave equation with time-periodic perturbation and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Yavar Kian","submitted_at":"2011-03-13T17:11:09Z","abstract_excerpt":"Consider the wave equation $\\partial_t^2u-\\Delta_xu+V(t,x)u=0$, where $x\\in\\R^n$ with $n\\geq3$ and $V(t,x)$ is $T$-periodic in time and decays exponentially in space. Let $ U(t,0)$ be the associated propagator and let $R(\\theta)=e^{-D<x>}(U(T,0)-e^{-i\\theta})^{-1}e^{-D<x>}$ be the resolvent of the Floquet operator $U(T,0)$ defined for $\\im(\\theta)>BT $ with $B>0$ sufficiently large. We establish a meromorphic continuation of $R(\\theta)$ from which we deduce the asymptotic expansion of $e^{-(D+\\epsilon)<x>}U(t,0)e^{-D<x>}f$, where $f\\in \\dot{H}^1(\\R^n)\\times L^2(\\R^n)$, as $t\\to+\\infty$ with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2530","kind":"arxiv","version":3},"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":"1103.2530","created_at":"2026-05-18T04:16:22.531923+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.2530v3","created_at":"2026-05-18T04:16:22.531923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2530","created_at":"2026-05-18T04:16:22.531923+00:00"},{"alias_kind":"pith_short_12","alias_value":"IX2FPEANE6NX","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"IX2FPEANE6NXP5XP","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"IX2FPEAN","created_at":"2026-05-18T12:26:32.869790+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/IX2FPEANE6NXP5XPB3AY3BNNNK","json":"https://pith.science/pith/IX2FPEANE6NXP5XPB3AY3BNNNK.json","graph_json":"https://pith.science/api/pith-number/IX2FPEANE6NXP5XPB3AY3BNNNK/graph.json","events_json":"https://pith.science/api/pith-number/IX2FPEANE6NXP5XPB3AY3BNNNK/events.json","paper":"https://pith.science/paper/IX2FPEAN"},"agent_actions":{"view_html":"https://pith.science/pith/IX2FPEANE6NXP5XPB3AY3BNNNK","download_json":"https://pith.science/pith/IX2FPEANE6NXP5XPB3AY3BNNNK.json","view_paper":"https://pith.science/paper/IX2FPEAN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.2530&json=true","fetch_graph":"https://pith.science/api/pith-number/IX2FPEANE6NXP5XPB3AY3BNNNK/graph.json","fetch_events":"https://pith.science/api/pith-number/IX2FPEANE6NXP5XPB3AY3BNNNK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IX2FPEANE6NXP5XPB3AY3BNNNK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IX2FPEANE6NXP5XPB3AY3BNNNK/action/storage_attestation","attest_author":"https://pith.science/pith/IX2FPEANE6NXP5XPB3AY3BNNNK/action/author_attestation","sign_citation":"https://pith.science/pith/IX2FPEANE6NXP5XPB3AY3BNNNK/action/citation_signature","submit_replication":"https://pith.science/pith/IX2FPEANE6NXP5XPB3AY3BNNNK/action/replication_record"}},"created_at":"2026-05-18T04:16:22.531923+00:00","updated_at":"2026-05-18T04:16:22.531923+00:00"}