Kostenko O. Spectral analysis of singularly perturbed differential operators of the second order

In the dissertation, the spectral properties of two special classes of non-self-adjoint differential operators is investigated. Necessary and sufficient conditions of similarity to a self-adjoint operator are obtained for the singular Sturm-Liouville operators with indefinite weights. An example of the operator with the singular critical point zero is constructed. For special classes of weights the question on dependence between boundary conditions at zero and similarity of the corresponding operator to a self-adjoint or normal one is studied. The simplicity of the minimal symmetric M.G. Krein string operator was proven, and the spectral properties of non-self-adjoint extensions are studied.