The bitangential inverse input impedance problem for canonical systems, II: Formulas and examples

摘要

This paper continues the study of the bitangential inverse input impedance problem for canonical integral systems that was initiated in [ArD6]. The problem is to recover the system, given an input impedance matrix valued function c(lambda) (that belongs to the Caratheodory class of p x p matrix valued functions that are holomorphic and have positive real part in the open upper half plane) and a chain of pairs {b(3)(t) (lambda), b(4)(t) (lambda)} of entire inner p x p matrix valued functions (that are identified with the associated pairs of the second kind of the matrizant of the system). Formulas for recovering the underlying canonical integral systems are derived by reproducing kernel Hilbert space methods. A number of examples are presented. Special attention is paid to the case when c(lambda) is of Wiener class and also when it is both of Wiener class and rational.