论文标题
关于Shrödingerl-Systems原始Weyl-Titchmarsh功能的实现
On realization of the original Weyl-Titchmarsh functions by Shrödinger L-systems
论文作者
论文摘要
我们研究原始Weyl-Titchmarsh函数产生的实现$ M_ \ infty（Z）$和$M_α（Z）$。结果表明，Herglotz-nevanlinna函数$（-M_ \ infty（z））$和$（1/m_ \ infty（z））$可以实现，因为相应的ShrödingerL-Systems共享同一主要散布操作员的阻抗函数。这些L系统是明确提出的，并且与Dirichlet和Neumann边界问题有关。对于Herglotz-Nevanlinna函数$（-M_α（Z））$和$（1/M_α（Z））$，与混合边界问题有关的相似结果但与混合边界问题有关。在最小对称的shrödinger操作员是非负面的情况下，我们还获得了这些实现的一些其他特性。除此之外，我们还指出并证明具有相等的Boun \ dary参数的ShrödingerL系统的唯一性实现标准。也建立了两个ShrödingerL系统共享同一主要运营商的条件。示例说明所获得的结果的示例在本文的末尾提供了。
We study realizations generated by the original Weyl-Titchmarsh functions $m_\infty(z)$ and $m_α(z)$. It is shown that the Herglotz-Nevanlinna functions $(-m_\infty(z))$ and $(1/m_\infty(z))$ can be realized as the impedance functions of the corresponding Shrödinger L-systems sharing the same main dissipative operator. These L-systems are presented explicitly and related to Dirichlet and Neumann boundary problems. Similar results but related to the mixed boundary problems are derived for the Herglotz-Nevanlinna functions $(-m_α(z))$ and $(1/m_α(z))$. We also obtain some additional properties of these realizations in the case when the minimal symmetric Shrödinger operator is non-negative. In addition to that we state and prove the uniqueness realization criteria for Shrödinger L-systems with equal boun\-dary parameters. A condition for two Shrödinger L-systems to share the same main operator is established as well. Examples that illustrate the obtained results are presented in the end of the paper.
