The riemann boundary problem with a complex orthogonal matrix

The Riemann boundary problem is studied under the assumption that the coefficient of the problem is a complex orthogonal matrix. In this case a property of the partial indices of the problem is established together with certain properties of the canonical matrices, which are then used to construct the canonical matrix of a complex orthogonal matrix of second order.Translated from Matematicheskie Zametki, Vol. 23, No. 3, pp. 405–416, March, 1978.The authors thank É. I. Zverovich, G. S. Litvinchuk, and I. M. Spitkovskii for helpful advice and remarks.