Matrix functions with arbitrarily prescribed left and right partial indices (Q1969962)

The main result is as follows. Given two vectors \(\rho, \lambda \in Z^n, n \geq 2,\) there exists a matrix function in \(L^\infty_{n \times n}\) on the unit circle which has the right Wiener-Hopf factorization in \(L^2\) with partial indices \(\rho\) and the left Wiener-Hopf factorization in \(L^2\) with partial indices \(\lambda\).