Non-selfadjoint matrix Sturm–Liouville operators with spectral singularities

摘要

In this paper we investigate discrete spectrum of the non-selfadjoint matrix Sturm–Liouville operator L generated in L2(R+,S) by the differential expressionℓ(y)=-y″+Q(x)y,x∈R+:[0,∞),and the boundary condition y(0)=0. Under the conditionsupx∈R+expεx‖Q(x)‖<∞,ε>0using the uniqueness theorem of analytic functions we prove that L has a finite number of eigenvalues and spectral singularities with finite multiplicities.