Kovalyov I. Indefinite Stieltjes moment problems and generalized Jacobi matrices

The indefinite Stieltjes moment problems and the Darboux transformation of generalized Jacobi matrices were studied. Schur step-by-step algorithm was constructed and a complete description of the solutions of the indefinite Stieltess moments problem in the generalized Stieltess class was obtained. The operator approach was applied to this problem, the factorization of resolvent matrices of the Stielttes moments problem was obtained in terms of u-resolvent M.G. Kerina The Darboux transformation of generalized Jacobi matrices was also investigated, the criterion for the existence of this transformation, the factorization of the Jacobi matrix and the explicit formulas for the transformation of the m-function, the first polynomial of the second kind, were obtained.