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Invariant Subspaces on ${{\mathbb{T}}^{N}}$ and ${{\mathbb{R}}^{N}}$
Published online by Cambridge University Press: 20 November 2018
Abstract
Let $N$ be an integer which is larger than one. In this paper we study invariant subspaces of ${{L}^{2}}({{\mathbb{T}}^{N}})$ under the double commuting condition. A main result is an $N$-dimensional version of the theorem proved by Mandrekar and Nakazi. As an application of this result, we have an $N$-dimensional version of Lax's theorem.
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- Copyright © Canadian Mathematical Society 2004
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