Neiman I. Abstract interpolation problem in the generalized Nevanlinna classes

The thesis is devoted to the study of the operator approach to interpolation problems in generalized Nevanlinna classes. A functional model for a self-adjoint linear relation in a reproducing kernel Pontryagin space is constructed as a tool for solution of an abstract interpolation problem. The set of all solutions of abstract interpolation problem is parameterized in the form of a linear fractional transformation of an arbitrary Nevanlinna pair. The method of abstract interpolation problem is applied to the full indefinite moment problem. An explicit formula for the resolvent matrix of the indefinite moment problem is found. In the thesis the concept of generalized matrix Smirnov classes is introduced and an analogue of Rouche's theorem for matrix functions of these classes is proved. A new generalized tangent interpolation problem in the classes of matrix Schur functions is considered. This auxiliary problem is used in order to describe the excluded parameters of indefinite tangent Schur-Takagi interpolation problems.