Invariance and near invariance for non-cyclic shift semigroups

2024/08/16 by Yuxia Liang, Jonathan R. Partington, Liang, Yuxia +2
Computer Science · Mathematics · #Advanced Topics in Algebra #Nonlinear Differential Equations Analysis #math.CV #math.FA #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2408.08659

openalex publication_date 2024/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterise the subspaces of H²(\mathbb D) that are invariant under the semigroups generated by two higher-order shifts S^m and Sⁿ. 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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