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- W3138145666 abstract "Let $H^2(mathbb{D}^n)$ denote the Hardy space over the polydisc $mathbb{D}^n$, $n geq 2$. A closed subspace $mathcal{Q} subseteq H^2(mathbb{D}^n)$ is called Beurling quotient module if there exists an inner function $theta in H^infty(mathbb{D}^n)$ such that $mathcal{Q} = H^2(mathbb{D}^n) /theta H^2(mathbb{D}^n)$. We present a complete characterization of Beurling quotient modules of $H^2(mathbb{D}^n)$: Let $mathcal{Q} subseteq H^2(mathbb{D}^n)$ be a closed subspace, and let $C_{z_i} = P_{mathcal{Q}} M_{z_i}|_{mathcal{Q}}$, $i=1, ldots, n$. Then $mathcal{Q}$ is a Beurling quotient module if and only if [ (I_{mathcal{Q}} - C_{z_i}^* C_{z_i}) (I_{mathcal{Q}} - C_{z_j}^* C_{z_j}) = 0 qquad (i neq j). ] We present two applications: first, we obtain a dilation theorem for Brehmer $n$-tuples of commuting contractions, and, second, we relate joint invariant subspaces with factorizations of inner functions. All results work equally well for general vector-valued Hardy spaces." @default.
- W3138145666 created "2021-03-29" @default.
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- W3138145666 date "2021-03-25" @default.
- W3138145666 modified "2023-09-25" @default.
- W3138145666 title "Beurling quotient modules on the polydisc" @default.
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