Linear Schrödinger equation with an almost periodic potential

2019/10/27 by Montalto, Riccardo, Procesi, Michela · 1 citation
#35B15 #35B35 #37K55 #46E50 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1910.12300

Abstract

We study the reducibility of a Linear Schrödinger equation subject to a small unbounded almost-periodic perturbation which is analytic in time and space. Under appropriate assumptions on the smallness, analiticity and on the frequency of the almost-periodic perturbation, we prove that such an equation is reducible to constant coefficients via an analytic almost-periodic change of variables. This implies control of both Sobolev and Analytic norms for the solution of the corresponding Schrödinger equation for all times.

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