We show that for a Jacobi operator with coefficients whose (j+1)th moments are summable the jth derivative of the scattering matrix is in the Wiener algebra of functions with summable Fourier coefficients. We use this result to improve the known disp
ersive estimates with integrable time decay for the time dependent Jacobi equation in the resonant case.
We show that for a one-dimensional Schrodinger operator with a potential whose (j+1)th moment is integrable the jth derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to im
prove the known dispersive estimates with integrable time decay for the one-dimensional Schrodinger equation in the resonant case.
