We investigate the spectrum of the differential operatorLλdefined by the Klein-Gordons-wave equationy″+(λ−q(x))2y=0,x∈ℝ+=[0,∞), subject to the spectral parameter-dependent boundary conditiony′(0)−(aλ+b)y(0)=0in the spaceL2(ℝ+), wherea≠±i,bare complex constants,qis a complex-valued function. Discussing the spectrum, we prove thatLλhas a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditionslimx→∞q(x)=0,supx∈R+{exp(ϵx)|q′(x)|}<∞,ϵ>0, hold. Finally we show the properties of the principal functions corresponding to the spectral singularities.
Spectral Properties of Discrete Klein–Gordon s-Wave Equation with Quadratic Eigenparameter-Dependent Boundary Condition
