论文标题
关于复数和四元组的伪谱分解
On Pseudo-Spectral Factorization over the Complex Numbers and Quaternions
论文作者
论文摘要
本文是对我们先前工作的研究的延续，并考虑了Quaternionic广义carathéodory函数和相关的广义积极功能。它涉及广泛的受众，其中包括线性系统理论的复杂和超复杂分析的研究人员，也包括电力工程师。因此，它包括有关广义carathéodory函数的一些结果及其在经典复杂案例中的分解，这可能引起了独立的兴趣。一个重要的新结果是伪谱分解，我们还讨论了Quaternionic广义阳性功能类别中的一些插值问题。
This paper is a continuation of the research of our previous work and considers quaternionic generalized Carathéodory functions and the related family of generalized positive functions. It is addressed to a wide audience which includes researchers in complex and hypercomplex analysis, in the theory of linear systems, but also electric engineers. For this reason it includes some results on generalized Carathéodory functions and their factorization in the classic complex case which might be of independent interest. An important new result is a pseudo-spectral factorization and we also discuss some interpolation problems in the class of quaternionic generalized positive functions.
