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Reducibility of Schrödinger Equation on the Sphere
International Mathematics Research Notices ( IF 1 ) Pub Date : 2020-03-05 , DOI: 10.1093/imrn/rnz344
Roberto Feola 1 , Benoît Grébert 1
Affiliation  

In this article we prove a reducibility result for the linear Schrödinger equation on the sphere $\mathbb{S}^n$ 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. Letus note that, surprisingly, our result does not require the use of the pseudo-differential calculus although the perturbation is unbounded.

中文翻译:

球形Schrödinger方程的可约性

在本文中,我们证明了球形\\ mathbb {S} ^ n $上线性Schrödinger方程在时间扰动下的可约性。我们的结果包括无界摄动的情况,我们假设该摄动的阶数严格小于$ 1/2 $,并且满足一定的平价条件。据我们所知,这是一维方程具有无穷大扰动的少数可约性结果之一。Letus注意到,令人惊讶的是,尽管微扰是无限的,但我们的结果不需要使用伪微积分。
更新日期:2020-03-05
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