Spectral Expansion of a Non-Self-Adjoint Differential Operator on the Whole Axis

AbstractIn this article, we consider an operator L defined by the differential expressionℓy=−y″+qxy,x∈R=−∞,∞in L2(R), where q is a complex-valued function. Under the conditionsup−∞<x<∞expϵ|x|qx<∞,ϵ>0,we have proved a spectral expansion of L in terms of the principal functions, taking into account the spectral singularities. We have also investigated the convergence of the spectral expansion of L