Schur algorithm for Stieltjes indefinite moment problem

TL;DR

This paper applies the Schur algorithm to the indefinite Stieltjes moment problem, deriving explicit formulas for solutions and their representations as generalized Stieltjes continued fractions.

Contribution

It introduces a step-by-step Schur algorithm approach for solving the indefinite Stieltjes moment problem and provides explicit formulas for the resolvent matrix.

Findings

Solution set characterized via Schur algorithm

Explicit resolvent matrix formula derived

Solutions expressed as generalized Stieltjes continued fractions

Abstract

Nondegenerate truncated indefinite Stieltjes moment problem in the class $\mathbf{N}_{\kappa}^{k}$ of generalized Stieltjes functions is considered. To describe the set of solutions of this problem we apply the Schur step-by-step algorythm, which leads to the expansion of these solutions in generalized Stieltjes continuous fractions studied recently in \cite{DK15}. Explicit formula for the resolvent matrix in terms of generalized Stieltjes polynomials is found.