{"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"}