Factorization theorem for the transfer function of a 2x2 operator matrix with unbounded couplings

Factorization Theorem for the Transfer Function Associated with an Unbounded Non-Self-Adjoint 2x2 Operator Matrix

We construct operators which factorize the transfer function associated with a non-self-adjoint 2x2 operator matrix whose diagonal entries can have overlapping spectra and whose off-diagonal entries are unbounded operators.

无界算子的特征值渐近性。双光子量子 Rabi 模型

Eigenvalues asymptotics of unbounded operators. Two-photon quantum Rabi model

本文研究无界算子在紧、相对紧及非紧等扰动下的特征值渐近性，推广 Janas-Naboko 引理，并以双光子量子 Rabi 模型为例给出能量算子大特征值三项渐近公式及相关多项式渐近性。

关于无衰减无界连续时间信号的预测器与滤波器

On predictors and filters for non-decaying unbounded continuous time signals

本文研究了在无穷远处不一定有界的非衰减连续时间信号的谱表示，为其引入了传递函数等概念，并给出了低通、高通滤波器及预测器的显式传递函数公式。

无界算子在 $S$-谱上的调和与多解析函数演算

Harmonic and polyanalytic functional calculi on the $S$-spectrum for unbounded operators

本文将四元数情形下基于切片超全纯 Cauchy 公式定义的 $S$-谱调和与多解析函数演算推广至无界交换算子，并证明其关键性质。

来自双对角分解的矩阵连分数

Positive Bidiagonal Factorizations: Combinatorial Structure, Spectral Theory, and Matrix Continued Fractions

本文从有序双对角分解构造矩阵连分数，通过循环线性化和有理高度排序转化为块三对角形式，截断得到 Padé 型逼近，并给出收敛性、残差估计及多种谱实现。

Darboux transformations of Jacobi matrices and Padé approximation

Let J be a monic Jacobi matrix associated with the Cauchy transform F of a probability measure. We construct a pair of the lower and upper triangular block matrices L and U such that J=LU and the matrix J_c=UL is a monic generalized Jacobi matrix associated with the function F_c(z)=zF(z)+1. It turns out that the Christoffel transformation J_c of a bounded monic Jacobi matrix J can be unbounded. This phenomenon is shown to be related to the effect of accumulating at infinity of the poles of the Padé approximants of the function F_c although F_c is holomorphic at infinity. The case of the UL-fac…