Abstract: | The theory of a matrix-valued function ( ), j-elementary in the unit circle and having a pole at the point 0, ¦ 0¦=1, on the boundary of the unit circle, is considered. The structure of ( ) is determined, conditions for the splittingoff of ( ) from an arbitrary matrix-valued function W( ), j-expanding in ¦ |< 1, are formed, a theorem on the parametrization of a j-elementary matrix-valued function ( ) of full rank is proved, and a decomposition of ( ) of full rank into the product of parametrized j-elementary factors of full rank with simple poles at the point 0 is found.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 62–74, 1988. |