有界解析函数下的不变性
Invariance Under Bounded Analytic Functions
摘要：
在最近的一篇论文中，M。Raghupathi延长了著名的定理Beurling的背景下，子空间是不变的下一类子代数的$H^\infty$的形式$IH^\infty$，其中$I$是一个内部功能。本文在一致代数、紧紧阿贝尔群群、实直线上的Lebesgue空间以及空间$BMOA$的背景下，给出了Beurling定理的上述$IH^\infty$相关推广的类似结果.我们还提供了一个显着的简化的证明的Beurling定理的设置一致代数和一个新的证明的Helson-Lowdenslager定理，推广Beurling定理的上下文中的紧阿贝尔群与有序群。
英文摘要：
In a recent paper, M. Raghupathi has extended the famous theorem of Beurling to the context of subspaces that are invariant under the class of subalgebras of $H^\infty$ of the form $IH^\infty$, where $I$ is an inner function. In this paper, we provide analouges of the above mentioned $IH^\infty$ related extension of Beurling's theorem to the context of uniform algebras, on compact abelian groups with ordered duals, the Lebesgue space on the real line and in the setting of the space $BMOA$. We also provide a significant simplification of the proof of the Beurling's theorem in the setting of uniform algebras and a new proof of the Helson-Lowdenslager theorem that generalizes Beurling's theorem in the context of compact abelian groups with ordered duals.
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