The Bitangential Inverse Input Impedance Problem for Canonical Systems, I: Weyl-Titchmarsh Classification, E*istence and Uniqueness

The inverse input impedance problem is investigated in the class of canonical integral systems with matrizants that are strongly regular J-inner matri* valued functions in the sense introduced in [ArD1]. The set of solutions for a problem with a given input impedance matri* (i.e., Weyl- Titchmarsh function) is parameterized by chains of associated pairs of entire inner p × p matri* valued functions. In our considerations the given data for the inverse bitangential input impedance problem is such a chain and an input impedance matri*, i.e., a p × p matri* valued function in the Caratheodory class. E*istence and uniqueness theorems for the solution of this problem are obtained by consideration of a corresponding family of generalized bitangential Caratheodory interpolation problems. The connection between the inverse bitangential input scattering problem that was studied in [ArD4] and the bitangential input impedance problem is also e*ploited. The successive sections deal with: 1. The introduction, 2. Domains of linear fractional transformations, 3. Associated pairs of the first and second kind, 4. Matri* balls, 5. The classification of canonical systems via the limit ball, 6. The Weyl-Titchmarsh characterization of the input impedance, 7. Applications of interpolation to the bitangential inverse input impedance problem. Formulas for recovering the underlying canonical integral systems, e*amples and related results on the inverse bitangential spectral problem will be presented in subsequent publications.