Factorization of matrices depending on a parameter, and elliptic equations in a halfspace

In this paper we prove the theorem that every matrix-function on the circle depending on a parameter admits a triangular factorization which is continuous in the parameter. Using this theorem, we manage to construct explicitly a regularizer of the boundary value problem for an elliptic system of pseudo-differential equations in a halfspace.
Figures: 8.
Bibliography: 16 titles.