α − regular indefinite Stieltjes moment problem and Darboux transformation

A sequence of the real numbers s = \{ si\}\ell i=0 is associated with the some
indefinite Stieltjes moment problem and generalized Jacobi matrices. The relation
between the \alpha - regular indefinite Stieltjes moment problem and shifted Darboux
transformation of the generalized Jacobi matrix is studied. The new formulas for
the Stieltjes polynomials with the shift are found and one are used to obtain the
description of the solutions of the \alpha - regular indefinite Stieltjes moment problem.