Criterion of unitary similarity of minimal passive scattering systems with a given transfer function (Q2730502)

The authors find necessary and sufficient conditions upon an operator-function \(\theta (z)\) of the Schur class for the unitary equivalence of all minimal passive scattering systems, for which \(\theta\) is a transfer function. The conditions are then simplified for some special cases, in particular if \(\theta\) is pseudo-continuable. If \(\theta\) is scalar and non-inner, the unitary equivalence is equivalent to the property of the function NEWLINE\[NEWLINE \frac{\overline{\theta (\zeta)}}{1-|\theta (\zeta)|^2},\quad |\zeta|=1, NEWLINE\]NEWLINE to be a boundary value of a function from the Smirnov class.