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

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