Spectral properties of a differential system

The spectrum of the differential operators associated with the differential systemu′=rDDpu, Dy=−y″+qy on L2([0,∞))is determined. For this the coefficients are assumed to satisfy rather general properties which combine smoothness and decay. With this the asymptotics of the eigenfunctions can be determined. This in turn leads to properties of the spectra with the aid of the M-matrix.