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arXiv · 2408.08659

Invariance and near invariance for non-cyclic shift semigroups

Yuxia Liang·Jonathan R. Partington
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Abstract

We characterise the subspaces of $H^2(\mathbb D)$ that are invariant under the semigroups generated by two higher-order shifts $S^m $ and $S^{n}$. Complete descriptions are obtained for both invariant and nearly invariant subspaces associated with these operators and their adjoints. The approach is based on vector-valued Hardy spaces, the Beurling--Lax theorem, and matrix-valued inner functions. Finally we apply these results to non-cyclic shift semigroups and to Toeplitz operators induced by finite Blaschke products.

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Yuxia Liang, Jonathan R. Partington. 2024-08-16. Invariance and near invariance for non-cyclic shift semigroups. https://arxiv.org/abs/2408.08659

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