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MR1736195 35P25 (35J10 35Q55 47A40 47F05)
Weder, Ricardo $L^p$-$L^{\dot p}$ estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential. J. Funct. Anal. 170 (2000), no. 1, 37–68.
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