Spectrum and principal functions of the non-self-adjoint Sturm-Liouville operators with a singular potential

We consider the operator L generated in L2(R+) by the differential expression l(y)=−y″+[ν2−14x2+q(x)]y,x∈R+≔(0,∞) and the boundary condition limx→0x−ν−12y(x)=1, where q is a complex valued function and ν is a complex number with Reν>0. In this work we investigate the eigenvalues and the spectral singularities of L. We also obtain the properties of the principal functions corresponding to the spectral singularities of L.