Invariant subspaces of ${\mathcal{H}}^2({\mathbb{T}}^2)$ and $L^2({\mathbb{T}}^2)$ preserving compatibility

Abstract

Operators of multiplication by independent variables on the space of square summable functions over the torus and its Hardy subspace are considered. Invariant subspaces where the operators are compatible are described.

17 pages, 3 figures

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