Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix

The inverse problem of recovering differential operators
$$ ly=y^{(n)}+\sum_{\nu=0}^{n-2}p_\nu(x)y^{(\nu)}, \qquad x>0, $$
from the Weyl matrix is investigated. A solution of this problem is given for arbitrary behavior of the spectrum, along with necessary and sufficient conditions and a uniqueness theorem.