Spectral properties of the Klein-Gordon \(s\)-wave equation with complex potential (Q1366931)

The operator \(L\) defined by the \(s\)-wave Klein-Gordon equation \(y''+[\lambda- Q(x)]^2y=0\), \(y(0)=0\), is considered, and its discrete spectrum discussed. It is proven that \(L\) has a finite number of eigenvalues and spectral singularities and each of them is of finite multiplicity. The principal functions corresponding to the eigenvalues \(\lambda\) and to the spectral singularities of \(L\) are constructed. The spectral expansion in terms of the principal functions of \(L\) will be treated in another article.