Invariant Subspaces on $mathbb{T}^N$ and $mathbb{R}^N$

[摘要] Let $N$ be an integer which is larger than one. In this paper westudy invariant subspaces of $L^2 (mathbb{T}^N)$ under the doublecommuting condition. A main result is an $N$-dimensional version ofthe theorem proved by Mandrekar and Nakazi. As an application of thisresult, we have an $N$-dimensional version of Lax's theorem.

[学科分类] 数学（综合）

[关键词] invariant subspaces