Dissipative eigenvalue problems for a singular Dirac system
Lax-Phillips scattering theory and Nagy-Foias' theory of functional models are used for the study of the spectral properties of maximal dissipative extensions of the minimal operator \(L_{0}\) generated by the differential expression \(l(y)=-y''(x)+Q(x)y(x)\) on \((-\infty,\infty)\). The matrix \(Q(x)\) is symmetric and its elements are real-valued and locally integrable on the real line. The author proves that almost all the maximal dissipative extensions of \(L_0\) have purely discrete spectrum included in the open upper half plane and that the system of eigenvectors and associated vectors of these extensions is complete.
scientific article; zbMATH DE number 2102860
scientific article