Dispersive estimates and asymptotic expansions for Schrödinger equations in dimension one

un 2 00 3 Dispersive estimates for Schrödinger operators in dimensions one and three

High frequency dispersive estimates in dimension two

We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrödinger groups for a very large class of real-valued potentials.

On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension

Abstract Based on the recent work [4] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator Hφ = (−∆+ V )φ = −(φn+1 + φn−1 − 2φn) + Vnφn. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicit...

Comparison of Estimates for Dispersive Equations

This paper describes a new comparison principle that can be used for the comparison of space-time estimates for dispersive equations. In particular, results are applied to the global smoothing estimates for several classes of dispersive partial differential equations.

Asymptotic expansions for degenerate parabolic equations

Article history: Received 14 May 2014 Accepted after revision 26 September 2014 Available online 11 October 2014 Presented by Olivier Pironneau We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the unifo...