Dispersion Estimates for One-Dimensional Schrödinger and Klein-Gordon Equations Revisited

Abstract

We show that for a one-dimensional Schrödinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive dispersion estimates for solutions of the associated Schrödinger and Klein-Gordon equations. In particular, we remove the additional decay conditions in the case where a resonance is present at the edge of the continuous spectrum.

21 pages

References in corpus (5)

• Resonances, Radiation Damping and Instability in Hamiltonian Nonlinear Wave Equations
• Dispersive estimates for Schrodinger operators in dimensions one and three
• L^p boundedness of the wave operator for the one dimensional Schroedinger operator
• Asymptotic stability of Landau solutions to Navier-Stokes system
• Dispersion Estimates for One-dimensional Discrete Schrödinger and Wave Equations

Cited by in corpus (3)

• The $1$d nonlinear Schrödinger equation with a weighted $L^1$ potential
• Attractors of Hamilton nonlinear partial differential equations
• Sine-Gordon on a wormhole