Dispersive estimates and asymptotic expansions for Schrödinger equations in dimension one. (English) Zbl 1211.35092
Summary: We study the time decay of scattering solutions to one-dimensional Schrödinger equations and prove a weighted dispersive estimate with stronger time decay than the case of unweighted estimates for the non-resonant state. Furthermore, asymptotic expansions in time of scattering solutions are given. The key of the proof is the study of the Fourier properties of Jost functions. We improve the Fourier properties of Jost functions obtained by P. D’Ancona and L. Fanelli [Commun. Math. Phys. 268, No. 2, 415–438 (2006; Zbl 1127.35053)].
MSC:
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35B45 | A priori estimates in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35C20 | Asymptotic expansions of solutions to PDEs |
Citations:
Zbl 1127.35053References:
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