论文标题
原始的Weyl-Titchmarsh功能和部门Shrödingerl-Systems
The original Weyl-Titchmarsh functions and sectorial Shrödinger L-systems
论文作者
论文摘要
在本文中，我们研究了原始的Weyl-Titchmarsh函数$M_α（Z）$在$ l_2 [\ ell，+\ infty）$中产生的L系统实现$M_α（Z）$是非负的。我们意识到函数$（-M_α（z））$作为Shrödingerl-systems的Ince \ - dance函数，并得出了$（-M_α（Z））$的必要条件，以属于sectorial类$ s^{β_1，β_1，β_2，β_2} $ stieltjes函数。此外，结果表明，$ m_ \ infty（-0）$和参数$α$的知识使我们能够描述实现$（-M_α（Z））$的L系统的几何结构。 L系统的主要和状态空间操作员意识到$（-M_α（Z））$具有相同或不具有部位角度的条件，以参数$α$表示。说明所获得结果的示例在本文的末尾提供了。
In this paper we study the L-system realizations generated by the original Weyl-Titchmarsh functions $m_α(z)$ in the case when the minimal symmetric Shrö\-dinger operator in $L_2[\ell,+\infty)$ is non-negative. We realize functions $(-m_α(z))$ as impe\-dance functions of Shrödinger L-systems and derive necessary and sufficient conditions for $(-m_α(z))$ to fall into sectorial classes $S^{β_1,β_2}$ of Stieltjes functions. Moreover, it is shown that the knowledge of the value $m_\infty(-0)$ and parameter $α$ allows us to describe the geometric structure of the L-system that realizes $(-m_α(z))$. Conditions when the main and state space operators of the L-system realizing $(-m_α(z))$ have the same or not angle of sectoriality are presented in terms of the parameter $α$. Example that illustrates the obtained results is presented in the end of the paper.
