{"paper":{"title":"A weighted dispersive estimate for Schr\\\"{o}dinger operators in dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Burak Erdo\\u{g}an, William R. Green","submitted_at":"2012-01-31T23:32:59Z","abstract_excerpt":"Let $H=-\\Delta+V$, where $V$ is a real valued potential on $\\R^2$ satisfying $|V(x)|\\les \\la x\\ra^{-3-}$. We prove that if zero is a regular point of the spectrum of $H=-\\Delta+V$, then $$ \\|w^{-1} e^{itH}P_{ac}f\\|_{L^\\infty(\\R^2)}\\les \\f1{|t|\\log^2(|t|)} \\|w f\\|_{L^1(\\R^2)},  |t| >2, $$ with $w(x)=\\log^2(2+|x|)$. This decay rate was obtained by Murata in the setting of weighted $L^2$ spaces with polynomially growing weights."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0050","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"}