{"paper":{"title":"A weighted estimate for two dimensional Schrodinger, matrix schrodinger and wave equations with resonance of first kind at zero energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ebru Toprak","submitted_at":"2015-09-10T15:57:20Z","abstract_excerpt":"We study the two dimensional Schr\\\"odinger operator, $H=-\\Delta+V$, in the weighted L^1(\\R^2) \\rightarrow L^{\\infty}(\\R^2) setting when there is a resonance of the first kind at zero energy. In particular, we show that if |V(x)|\\les \\la x \\ra ^{-3-} and there is only s-wave resonance at zero of H, then \\big\\| w^{-1} \\big( e^{itH}P_{ac} f - {\\f 1 t } F f \\big) \\big\\| _{\\infty} \\leq \\frac {C} {|t| (\\log|t|)^2 } \\|wf\\|_1 |t|>2, with w(x)=\\log^2(2+|x|). Here Ff=c \\psi\\la f,\\psi \\ra, where \\psi is an s-wave resonance function. We also extend this result to matrix Schr\\\"odinger and wave equations wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03204","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"}