Андреищева Е. Н.

The Problem of Factorization of Rational Matrix Functions for the Case of a Generalized Nevanlinna Class

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In the present paper, we consider $z_1$ as a fixed point in the open upper half
plane $\mathbb{C} ^+$. We study rational 2 × 2- matrix functions $\Theta(z)%$ which have a pole only in the point
$z^1_*$. Their entries are polynomials in $\frac{1}{(z-z^1_*)}$, and which are $J_l$ -unitary, that is, satisfy on the
real line:

$\Theta(z)J_l\Theta(z)^* = J_l$, $z \in \mathbb{R}$, $\mathbf{J_l} := \left(
\begin{array}{cc}
0 & 1 \\
-1 & 0 \\
\end{array} \right)$.