Hilbert Spaces Contractively Contained in Weighted Bergman Spaces on the Unit Disk

Unbounded multipliers of complete Pick spaces

We examine densely defined (but possibly unbounded) multiplication operators in Hilbert function spaces possessing a complete Nevanlinna-Pick (CNP) kernel. For such a densely defined operator $T$, the domains of $T$ and $T^*$ are reproducing kernel Hilbert spaces contractively contained in the ambient space. We study several aspects of these spaces, especially the domain of $T^*$, which can be viewed as analogs of the classical deBranges-Rovnyak spaces in the unit disk.

近不变布兰奇空间子空间

Nearly invariant brangesian subspaces

本文将Hitt关于$H^2(\bb D)$上后移算子近不变子空间的定理及其推广扩展到布兰奇空间框架，研究开单位圆盘上解析函数再生核希尔伯特空间中被内函数除时近不变的压缩包含希尔伯特空间。

加权Bergman空间上Toeplitz算子与复合算子的数值域

Numerical range of Toeplitz and Composition operators on weighted Bergman spaces

本文完整刻画了加权Bergman空间上调和符号Toeplitz算子及加权复合算子的数值域，分类了复合算子数值域对应的集合，并研究了零的包含性及所含圆和椭圆的半径。

The Feichtinger Conjecture and Reproducing Kernel Hilbert Spaces

We prove two new equivalences of the Feichtinger conjecture that involve reproducing kernel Hilbert spaces. We prove that if for every Hilbert space, contractively contained in the Hardy space, each Bessel sequence of normalized kernel functions can be partitioned into finitely many Riesz basic sequences, then a general bounded Bessel sequence in an arbitrary Hilbert space can be partitioned into finitely many Riesz basic sequences. In addition, we examine some of these spaces and prove that for these spaces bounded Bessel sequences of normalized kernel functions are finite unions of Riesz bas…

Multiplication operators on the Bergman space via analytic continuation

In this paper, using the group-like property of local inverses of a finite Blaschke product $ϕ$, we will show that the largest $C^*$-algebra in the commutant of the multiplication operator $M_ϕ$ by $ϕ$ on the Bergman space is finite dimensional, and its dimension equals the number of connected components of the Riemann surface of $ϕ^{-1}\circϕ$ over the unit disk. If the order of the Blaschke product $ϕ$ is less than or equal to eight, then every $C^*$-algebra contained in the commutant of $M_ϕ$ is abelian and hence the number of minimal reducing subspaces of $M_ϕ$ equals the number of connect…

伯格曼再生核的最优非对角线上界估计

Optimal off-diagonal upper estimates for Bergman reproducing kernels

研究单位圆盘上伯格曼再生核的非对角线上界估计，基于权重矩的单边加倍条件证明其精确性及刻画性。通过新方法得到修正伯格曼核的\(L^p\)均值估计，建立相关函数与测度新联系，还将结果推广到高维等情况。