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• W2215703453 abstract "We study the two dimensional Schrodinger 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 psila f,psi ra, where psi is an s-wave resonance function. We also extend this result to matrix Schrodinger and wave equations with potentials under similar conditions." @default.
• W2215703453 created "2016-06-24" @default.
• W2215703453 creator A5069727861 @default.
• W2215703453 date "2017-12-08" @default.
• W2215703453 modified "2023-09-27" @default.
• W2215703453 title "A weighted estimate for two dimensional Schrödinger, matrix Schrödinger, and wave equations with resonance of the first kind at zero energy" @default.
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• W2215703453 doi "https://doi.org/10.4171/jst/189" @default.
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