Dyukarev Y. The theory of interpolation problems in the Stieltjes class and adjacent analysis problems

Objects: interpolation problems in the Nevanlinna, Stiltjes and Krein classes and defective numbers of the symmetrical operators. Goals: to build the theory of the interpolation problems in the Stiltjes class and to solve some of the problems. Investigation of the defective numbers of the Jacobi matrices. Methods: methods of the Hilbert spaces operator theory, the theory of matrix measures, the theory of factorization of J-extending matrix functions. New theoretical results: the theory of the Stiltjes function is built. The limit interpolation problem for the Nevanlinna functions is investigated. The complete description of the defective numbers of the block matrix Jacobi is obtained. The matrix moment problem on the compact interval is solved. Employment. The results may be applied in the moment problem, in the interpolation theory, for investigation of the defective numbers of the symmetrical operators and in the theory of the orthogonal matrix functions.