论文标题
伯格曼（Bergman）转移的流浪子空间中功能的表征通过bidisc的强壮空间
Characterizations of functions in wandering subspaces of the Bergman Shift via the Hardy space of the Bidisc
论文作者
论文摘要
令$ \ Mathcal {w} $为伯格曼移动不变子空间的相应流浪子空间。通过用$ h^2（\ mathbb {d}^2）\ aminus [z-w] $识别伯格曼的空间，这是$ h^2（\ mathbb {d}^2）的封闭子空间的足够且必要的条件给出了流浪子空间。作为一个副产品，我们证明了两个不变子空间$ \ MATHCAL {M} $，$ \ MATHCAL {N} $，带有$ \ Mathcal {M} \ supsetneq \ supsetneq \ Mathcal {n} $ $ dim（\ Mathcal {m} \ ominus b \ Mathcal {m}）= \ infty $，然后有一个不变的子空间$ \ nathcal {l} $，这样$ \ m athcal {m} \ mathcal {m} \ supsetneq \ supsetneq \ supscal {l} l} {l} {l} \ supsetne} $} $} $}。最后，我们将操作员从一个流浪子空间定义到另一个流浪子空间，并为与伯格曼（Bergman）偏移的通用属性相关的操作员获得分解定理。
Let $\mathcal{W}$ be the corresponding wandering subspace of an invariant subspace of the Bergman shift. By identifying the Bergman space with $H^2(\mathbb{D}^2)\ominus[z-w]$, a sufficient and necessary conditions of a closed subspace of $H^2(\mathbb{D}^2)\ominus[z-w]$ to be a wandering subspace of an invariant subspace is given also, and a functional charaterization and a coefficient characterization for a function in a wandering subspace are given. As a byproduct, we proved that for two invariant subspaces $\mathcal{M}$, $\mathcal{N}$ with $\mathcal{M}\supsetneq\mathcal{N}$ and $dim(\mathcal{N}\ominus B\mathcal{N})<\infty$ $dim(\mathcal{M}\ominus B\mathcal{M})=\infty$, then there is an invariant subspace $\mathcal{L}$ such that $\mathcal{M}\supsetneq\mathcal{L}\supsetneq\mathcal{N}$. Finally, we define an operator from one wandering subspace to another, and get a decomposition theorem for such an operator which is related to the universal property of the Bergman shift.
