A remark to the definition of Nevanlinna matrices

Анотація

We prove that the unimodular entire matrix-function\begin{equation*}
\left(\begin{array}{cc}
A(z)&B(z)\\ C(z)& D(z)
\end{array}\right)
\end{equation*}with real entries is a Nevanlinna matrix provided that the three quotients B/A, A/C and D/C have positive imaginary part in the upper half-plane.