Zero Energy Scattering for One-Dimensional Schrödinger Operators and Applications to Dispersive Estimates

Abstract

We show that for a one-dimensional Schrödinger operator with a potential whose (j+1)'th moment is integrable the j'th derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to improve the known dispersive estimates with integrable time decay for the one-dimensional Schrödinger equation in the resonant case.

9 pages

References in corpus (5)

• Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent
• Asymptotic stability of Landau solutions to Navier-Stokes system
• Dispersion Estimates for One-dimensional Discrete Schrödinger and Wave Equations
• Semiclassical analysis of low and zero energy scattering for one dimensional Schrödinger operators with inverse square potentials
• Properties of the Scattering Matrix and Dispersion Estimates for Jacobi Operators