The paper deals with the Schur algorithm of solution of the indefinite truncated moment problem. The main theorem describes the inductive step which reduces the original problem to a problem in a smaller dimension. The algorithm leads to a factorization of the corresponding solution matrix.

The paper deals with two types of inverse spectral problems for the class of generalized Jacobi matrices introduced in [9]. Following the scheme proposed in [5], we deduce analogs of the Hochstadt - Lieberman theorem and the Borg theorem. Properties of a Weyl function of the generalized Jacobi matrix are systematically used to prove the uniqueness theorems. Trace formulas for the generalized Jacobi matrix are also derived.