A truncated indefinite Stieltjes moment problem

Abstract

A truncated indefinite Stieltjes moment problem in the class \( {\mathrm{N}}_{\kappa}^k \) of generalized Stieltjes functions is studied. The set of solutions of the Stieltjes moment problem is described by the Schur stepby-step algorithm, which is based on the expansion of the solutions in a generalized Stieltjes continued fraction. The resolvent matrix is represented in terms of generalized Stieltjes polynomials. A factorization formula for the resolvent matrix is found.