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

Published:2004-03-01
Printed: Mar 2004
• Michio Seto
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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.
 Keywords: invariant subspaces invariant subspaces
 MSC Classifications: 47A15 - Invariant subspaces [See also 47A46] 47B47 - Commutators, derivations, elementary operators, etc.