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• W2997268082 abstract "We prove that the wave operators for $n times n$ matrix Schrödinger equations on the half line, with general selfadjoint boundary condition, are bounded in the spaces $L^p(mathbb R^+, mathbb C^n),$ $1 < p < infty,$ for slowly decaying selfadjoint matrix potentials $V$ that satisfy the condition $int_{0}^{infty}(1+x) |V(x)|: dx < infty.$ Moreover, assuming that $int_{0}^{infty }(1+x^gamma) |V(x)|: dx < infty,$ $gamma > frac{5}{2},$ and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in $L^1(mathbb R^+, mathbb C^n)$ and in $L^infty(mathbb R^+, mathbb C^n).$ We also prove that the wave operators for $ntimes n$ matrix Schrödinger equations on the line are bounded in the spaces $L^p(mathbb R, mathbb C^n), 1 < p < infty,$ assuming that the perturbation consists of a point interaction at the origin and of a potential $mathcal V$ that satisfies the condition $int_{-infty}^{infty}(1+|x|)|mathcal V(x)|: dx < infty.$ Further, assuming that $int_{-infty}^{infty }(1+|x|^gamma) |mathcal V(x)|: dx < infty,$ $gamma > frac{5}{2},$ and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in $L^1(mathbb R, mathbb C^n)$ and in $L^infty(mathbb R, mathbb C^n).$ We obtain our results for $ntimes n$ matrix Schrödinger equations on the line from the results for $2ntimes 2n$ matrix Schrödinger equations on the half line." @default.
• W2997268082 created "2020-01-10" @default.
• W2997268082 creator A5029382973 @default.
• W2997268082 date "2022-09-21" @default.
• W2997268082 modified "2023-09-30" @default.
• W2997268082 title "The $L^p$ boundedness of the wave operators for matrix Schrödinger equations" @default.
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• W2997268082 doi "https://doi.org/10.4171/jst/417" @default.
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