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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$G$$ \end{document}-regular self-adjoint extensions of the model symmetric operator associated with the problem is established. Sufficient conditions for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$G$$ \end{document}-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.