Patsiuk O. Elements of the theory of PT-symmetric operators

The thesis is devoted to the study of the spectral properties of abstract PT-symmetric operators depending on their representations as self-adjoint operators in Krein spaces with indefinite metrics defined using Clifford algebras. The work established the possibility of interpretation of a class of PT-symmetric operators as self-adjoint ones in the Krein spaces constructed by Clifford algebra Cl2, and the research of their spectral properties, depending on the quantity and "quality" of such interpretations. Also it has obtained criterion for a non-real number to belong to the point spectrum and found necessary and sufficient conditions for the existence of stable C-symmetry property for the PT-symmetric operators A at the mentioned class. The results were used to study the spectral properties of Schrodinger operators with PT-symmetric singular potentials.