Derevyagin M. Spectral analysis of generalized Jacobi matrices

The thesis is devoted to the study of generalized Jacobi matrices associated to the step-by-step process of solving an indefinite moment problem. The step-by-step process of solving the truncated indefinite moment problem is constructed. Generalized Jacobi matrices associated to the step-by-step process is introduced. Direct and inverse spectral problems for both finite and infinite generalized Jacobi matrices are studied. As a consequence of the elaborated theory of generalized Jacobi matrices, the results on the locally uniform convergence of diagonal and paradiagonal Pade approximants are obtained.