Yokuş, NihalArpat, Esra Kır2021-11-042021-11-042019-08-01https://doi.org/10.31801/cfsuasmas.526270http://hdl.handle.net/20.500.12575/75882In this paper, we consider the operator L generated in L₂(R₊) by the differential expression l(y)=-y′′+q(x)y,x∈R₊:=[0,∞) and the boundary condition ((y′(0))/(y(0)))=α₀+α₁λ+α₂λ², where q is a complex valued function and α_{i}∈C,[mbox]<LaTeX>\mbox{\:}</LaTeX>i=0,1,2α₂. We have proved that spectral expansion of L in terms of the principal functions under the condition q∈AC(R₊), lim_{x→∞}q(x)=0, sup[e^{ε√x}|q′(x)|]<∞, ε>0 taking into account the spectral singularities. We have also proved the convergence of the spectral expansion.enEigenvaluesSpectral singularitiesPrincipal functionsArticle682131613342618-6470