On Transformation of Potapov's Fundamental Matrix Inequality

TL;DR

This paper explores various transformations of Potapov's Fundamental Matrix Inequality (FMI) to better understand its solutions in classical interpolation problems, supported by illustrative examples.

Contribution

It introduces and motivates different transformations of the FMI, providing a clearer framework for solving interpolation problems.

Findings

Multiple transformations of FMI are effective in solving interpolation problems.

Transformations are motivated by and demonstrated through simple examples.

The approach clarifies the relationship between FMI solutions and interpolation solutions.

Abstract

According to V.P.Potapov, a classical interpolation problem can be reformulated in terms of a so-called Fundamental Matrix Inequality (FMI). To show that every solution of the FMI satisfies the interpolation problem, we usualy have to transform the FMI in some special way. In this paper the number of of transformations of the FMI which come into play are motivated and demonstrated by simple, but typical examples.