Reducibility of Schrödinger equation on the sphere

2019/05/28 by Feola, Roberto, Grébert, Benoît
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.11964

Abstract

In this article we prove a reducibility result for the linear Schrödinger equation on the sphere \mathbbSⁿ with quasi-periodic in time perturbation. Our result includes the case of unbounded perturbation that we assume to be of order strictly less than 1/2 and satisfying some parity condition. As far as we know, this is one of the few reducibility results for an equation in more than one dimension with unbounded perturbations. We notice that our result does not requires the use of the pseudo-differential calculus.

Related

• Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations, II
• Reducibility of relativistic Schrödinger equation with unbounded perturbations
• Linear Schrödinger equation with an almost periodic potential
• A reducibility result for Schrödinger operator with finite smooth and time quasi-periodic potential
• Reducibility of quantum harmonic oscillator on R^d with differential and quasi-periodic in time potential