加权后移不变子空间中的解析延拓与嵌入

Cowen-Douglas 算子与解析延拓

Cowen-Douglas operators and analytic continuation

本文研究了解析函数 Banach 空间上左可逆乘法算子的左逆作为 Cowen-Douglas 算子的条件，并探讨了该算子不变子空间中函数的解析延拓与其限制谱之间的关系。

星型不变子空间中的坏边界表现I

Bad boundary behavior in star invariant subspaces I

讨论了后移不变子空间$(B H^2)^{\perp}$中函数的边界表现，其中$B$是Blaschke积.扩展一些结果埃亨和克拉克，我们特别感兴趣的增长率的职能点的频谱$B$的地方$B$不承认衍生物的意义上的Carathéodory。

后移不变空间中的一致极小性、无条件性和插值

Uniform minimality, unconditionality and interpolation in backward shift invariant spaces

讨论了后移不变子空间中再生核族的一致极小性、无条件性和插值之间的关系。这类空间包含作为突出的例子Paley-Wiener空间，它是已知的，一致极小一般既不意味着插值也不无条件。因此，与标准哈代空间（以及其他空间尺度）的情况相反，在这种情况下，改变空间的大小似乎是从一致极小性推导无条件性或插值所必需的。这种变化可以采取两个方向：降低积分的幂，或“增加”定义内部函数（例如，增加Paley-Wiener空间的类型）。Khinchin不等式在我们主要结果的证明中起着重要的作用。

A Beurling Theorem for almost-invariant subspaces of the shift operator

A complete characterization of nearly-invariant subspaces of finite defect for the backward shift operator acting on the Hardy space is provided in the spirit of Hitt and Sarason's theorem. As a corollary we describe the almost-invariant subspaces for the shift and its adjoint.

Nearly invariant subspaces for operators in Hilbert spaces

For a shift operator $T$ with finite multiplicity acting on a separable infinite dimensional Hilbert space we represent its nearly $T^{-1}$ invariant subspaces in terms of invariant subspaces under the backward shift. Going further, given any finite Blaschke product $B$, we give a description of the nearly $T_{B}^{-1}$ invariant subspaces for the operator $T_B$ of multiplication by $B$ in a scale of Dirichlet-type spaces.

Do some nontrivial closed z-invariant subspaces have the division property ?

We consider Banach spaces E of functions holomorphic on the open unit disc D such that the unilateral shift S and the backward shift T are bounded on E. Assuming that the spectra of S and T are equal to the closed unit disc we discuss the existence of closed z-invariant of N of E having the "division property", which means that the function f $λ$ : z $\rightarrow$ f (z)/ z--$λ$ belongs to N for every $λ$ $\in$ D and for every f $\in$ N such that f ($λ$) = 0. This question is related to the existence of nontrivial bi-invariant subspaces of Banach spaces of hyperfunctions on the unit circle T.

光滑解析函数与模型子空间

Smooth analytic functions and model subspaces

本综述的主要主题如下：（a）圆盘上光滑到其边界的各类解析函数中的正则（Riesz-Nevanlinna）因子分解，以及（b）模型子空间（即，后移的不变子空间）在Hardy空间$H^p$和BMOA中。我们要强调的是这两个主题之间的相互关系和特殊的相互促进作用。