Generalized factorization for a class of non-rational 2\(\times 2\) matrix functions
The authors study the generalized factorization for the class of \(2\times 2\) piecewise continuous matrix functions on \({\dot {\mathbb{R}}}={\mathbb{R}}\cup \{\infty \}\) which are of the form \[ G=\left[ \begin{matrix} 1\\ {\bar \rho}_ a'\end{matrix} \quad \begin{matrix} \lambda a\rho \\ 1\end{matrix} \right], \] where \(\rho\) is a complex-valued function such that \(\rho^ 2\) is a rational function of the form \[ \rho^ 2=(\frac{\omega -k)}{\omega +k_ 1})^ n,\quad k,k_ 1\in {\mathbb{C}}\setminus {\mathbb{R}},\quad n\quad natural, \] \(a\) is an arbitrary piecewise continuous function and \(\lambda\in {\mathbb{C}}\). A space transformation is used to reduce the problem to the generalized factorization of a scalar piecewise continuous function on a contour in the complex plane.
scientific article; zbMATH DE number 4171125