Amirshadyan A. Interpolation problems in generelized Nevanlinna and Stieltjes classes

In this thesis we consider bitangential interpolation problems in generalized Nevanlinna and Stieltjes classes. For a simple Hermitian operator in a Pontryagin space, we proved that there exists its self-adjoint extension with the given regular points.An operator model for the Nevanlinna-Pick bitangential interpolation problem in generalized Nevanlinna and Stieltjes classes for both nondegenerate and degenerate cases is constructed. In the case of a nondegenerate Pick matrix, a description of all the solutions is obtained. The Nevanlinna-Pick boundary indefinite interpolation problem was investigated. In the case of a nondegenerate Pick matrix, we obtained a description of all its solutions.