Boundary Interpolation Problem in the Classes of Generalized Nevanlinna Matrix Functions

The paper deals with the boundary indefinite interpolation problem in the classes of generalized Nevanlinna matrix functions. A one-to-one correspondence between the set of all solutions of the problem and the class of so-called $G$-regular self-adjoint extensions of the model symmetric operator associated with the problem is established. Sufficient conditions for the $G$-regularity of self-adjoint extensions (in terms of the Weyl function) are given. A formula for the description of all the solutions of the problem is obtained.