Abstract
The sufficient conditions under which the S-matrix orthogonal part U(k) is real and even are proved. These conditions are required for generalization of the projection matrices method in the N×N Riemann–Hilbert boundary value problem, N=2,3,…,N<+∞. The dependence of the analytical properties of the orthogonal matrix U(k) on the S-matrix diagonal part is thoroughly considered. The examples in which the sufficient conditions are not realized and Re U(k)≠0, U(−k)=−U(k) are demonstrated.
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