Wiener-Hopf factorization for a group of exponentials of nilpotent matrices (Q1593659)

The generalized factorization for a group of \(2 \times 2\) matrix functions of the form \(g=I+\gamma N\) is studied. Here \(I\) denotes the \(2 \times 2\) identity matrix, \(N\) is a rational nilpotent matrix function, and \(\gamma\) represents a continuous function on the real line possessing equal limits at \(\pm \infty\). Canonical and non-canonical factorizations are considered. Explicit formulae are obtained for partial indices and the relevant factors in such factorizations. Necessary and sufficient conditions for existence of canonical factorization are established.