Geodesic
Invariant Subspaces on ${{\mathbb{T}}^{N}}$ and ${{\mathbb{R}}^{N}}$
Canadian mathematical bulletin, Tome 47 (2004) no. 1, pp. 100-107

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DOI

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.
DOI : 10.4153/CMB-2004-011-5
Mots-clés : 47A15, 47B47, invariant subspaces 
Seto, Michio. Invariant Subspaces on ${{\mathbb{T}}^{N}}$ and ${{\mathbb{R}}^{N}}$. Canadian mathematical bulletin, Tome 47 (2004) no. 1, pp. 100-107. doi: 10.4153/CMB-2004-011-5
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     title = {Invariant {Subspaces} on ${{\mathbb{T}}^{N}}$ and ${{\mathbb{R}}^{N}}$},
     journal = {Canadian mathematical bulletin},
     pages = {100--107},
     year = {2004},
     volume = {47},
     number = {1},
     doi = {10.4153/CMB-2004-011-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-011-5/}
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