Herglotz-Nevanlinna函数的连分数展开与Stieltjes型广义不定弦

由最优离散$p$-Hardy权导出的Herglotz-Nevanlinna函数

A Herglotz-Nevanlinna function from the optimal discrete $p$-Hardy weight

本文证明最优离散$p$-Hardy权对应Herglotz-Nevanlinna函数，建立其积分表示，并确认了相关绝对单调性猜想的修正。

A general realization theorem for matrix-valued Herglotz-Nevanlinna functions

New special types of stationary conservative impedance and scattering systems, the so-called non-canonical systems, involving triplets of Hilbert spaces and projection operators, are considered. It is established that every matrix-valued Herglotz-Nevanlinna function of the form V(z)=Q+Lz+\int_{\dR}(\frac{1}{t-z}-\frac{t}{1+t^2})dΣ(t) can be realized as a transfer function of such a new type of conservative impedance system. In this case it is shown that the realization can be chosen such that the main and the projection operators of the realizing system satisfy a certain commutativity conditio…

关于通过薛定谔L-系统实现原始Weyl-Titchmarsh函数的研究

On realization of the original Weyl-Titchmarsh functions by Shrödinger L-systems

该研究探讨原始Weyl-Titchmarsh函数通过薛定谔L-系统的实现问题，构造了对应不同边值问题的L-系统，推导了非负算子下的附加性质，给出了唯一性准则及主算子共享条件，并附示例说明。

Donoghue-Type $m$-Functions for Schrödinger Operators with Operator-Valued Potentials

Given a complex, separable Hilbert space $\mathcal{H}$, we consider self-adjoint $L^2$-realizations of differential expressions $τ= - (d^2/dx^2) I_{\mathcal{H}} + V(x)$, on half-lines and on the real line (assuming the limit-point property of $τ$ at $\pm \infty$). Here $V$ denotes a bounded operator-valued potential $V(\cdot) \in \mathcal{B}(\mathcal{H})$ such that $V(\cdot)$ is weakly measurable, the operator norm $\|V(\cdot)\|_{\mathcal{B}(\mathcal{H})}$ is locally integrable, and $V(\cdot) = V(\cdot)^*$ a.e. In a nutshell, a Donoghue-type $m$-function $M_{A,\mathcal{N}_i}^{Do}(\cdot)$ assoc…