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We show that for a one-dimensional Schr\"odinger operator with a potentialwhose (j+1)'th moment is integrable the j'th derivative of the scatteringmatrix is in the Wiener algebra of functions with integrable Fouriertransforms. We use this result to improve the known dispersive estimates withintegrable time decay for the one-dimensional Schr\"odinger equation in theresonant case.

Zero Energy Scattering for One-Dimensional Schr\"odinger Operators and Applications to Dispersive Estimates