Article

**Proc. Amer. Math. Soc. Ser. B 2, 51-59 (2015)**[DOI: 10.1090/bproc/19]

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

### Iryna Egorova, Markus Holzleitner, and Gerald Teschl

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.
** MSC2010:** Primary 34L25, 35Q41; Secondary 81U30, 81Q15

**Keywords:** *Schrödinger equation, scattering, resonant case, dispersive estimates*

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