发表机构
Schmid College of Science and Technology Chapman University; School of Electrical and Computer Engineering Ben-Gurion University of the Negev（查普曼大学施密德科学与技术学院; 内盖夫本-古里安大学电气与计算机工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究与正函数、有界函数相关的函数族，引入正函数子类与有界函数族的仿射线性关系，结合再生核希尔伯特空间等工具证明关联算子对的迹公式，为多学科领域研究者提供相关结果。
AI 中文摘要
我们研究一类带索引的函数族，它们与右开半平面内解析且具有正实部的函数（即所谓正函数）、以及右开半平面内解析且模不超过1的函数（即所谓有界函数）密切相关。这两类函数族通过Cayley变换关联。本文中，我们引入正函数的一个子类与有界函数族之间的仿射线性关系，并研究其与线性系统的无源性、插值及算子模型的对应联系。因此，本文是一篇多学科论文，潜在读者包括工程领域、线性系统理论及算子理论领域的研究者，文中重复了部分已知结果以方便各类读者阅读。解析函数的再生核希尔伯特空间是论证的关键工具，与有界函数关联的de Branges-Rovnyak空间发挥了特殊作用，我们还证明了一个相关的迹公式，其关联了底层的一对算子。
英文摘要
We study an indexed family of functions closely related to functions ana- lytic and with a real positive part in the right open half plane (the so-called positive functions) and to the functions analytic in the right open half-plane and bounded in modulus by one there (the so-called bounded functions). These two families are related by the Cayley transform. In the present paper we introduce an affine linear relation- ship between a subclass of positive functions and the family of bounded functions, and study the corresponding connections with passivity of linear systems, interpolation and operator models. This is therefore a multidisciplinary paper, with potential readers from engineering, linear system theory and operator theory, and some repetitions of known results are given to allow various audiences to read the work. Reproducing kernel Hilbert spaces of analytic functions are a key tool in the arguments. A special role is played by the de Branges-Rovnyak spaces associated to bounded functions, and we prove a related trace formula connecting an underlying pair of operators.
