Abstract:
The proposition about optimum factorization of a non-negative matrix function $f(\lambda)$ is generalized for the case where the unknown function $A(z)$ of class $H_2$ satisfies the inequality
$$
A(e^{-i\lambda})A^*(e^{-i\lambda})\leqq 2\pi f(\lambda)
$$
instead of the usual equality
$$
A(e^{-i\lambda})A^*(e^{-i\lambda})=2\pi f(\lambda).
$$