Frames containing a Riesz basis and preservation of this property under perturbation

Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$

We prove that a Hilbert space frame $\fti$ contains a Riesz basis if every subfamily $\ftj , J \subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements.

A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter

We establish a criterion for a set of eigenfunctions of the one-dimensional Schrödinger operator with distributional potentials and boundary conditions containing the eigenvalue parameter to be a Riesz basis for $\mathscr{L}_2(0,π)$.

正算子轨道的通用非均匀采样：基于完全Stein--Pick准则与密度

Density and Spectral Criteria for Universal Nonuniform Sampling of Positive Operator Orbits

本文通过Stein恒等式和双谱表示，利用径向Stein--Pick锥和密度条件，完整刻画了正算子轨道非均匀采样的通用精确可观测性，并揭示了谱相互作用导致的额外障碍及临界尺度。

保持正规对角算子轨道框架生成元的谱变换的边界刚性与分类

Carleson Interpolation, Boundary Rigidity, and Classification of Spectral Transformations Preserving Diagonal Operator Orbit Frames

该研究刻画了保持单位圆盘Carleson序列且满足伪双曲距离等价条件的映射类，证明其边界迹为双Lipschitz映射，给出核-角分解与半直积结构，明确多轨道保持类与单轨道一致，全纯成员为圆盘自同构，并提出可数情形的相关猜想。

关于$L^2(0,1)$中不构成Schauder基的精确系统$\{t^α\cdot e^{2πi nt}\}_{n\in\mathbb{Z}\setminus A}$及其推广

On exact systems $\{t^α\cdot e^{2πi nt}\}_{n\in\mathbb{Z}\setminus A}$ in $L^2 (0,1)$ which are not Schauder Bases and their generalizations

该研究针对$L^2(0,1)$空间，推导了去掉$M$个元素的加权指数Schauder基对偶系统为精确系统的$α$取值充要条件，证明其非Riesz基，且对应加权三角系统非Schauder基。