A Unified Treatment for the Matrix Stieltjes Moment Problem in Both Nondegenerate and Degenerate Cases

This paper presents a unified method for the solution of the matrix Stieltjes moment problem in both the nondegenerate and degenerate cases, based on the use of our recent investigation of the matrix Hamburger moment problem. As a by-product, a complete solution of the matrix Nevanlinna Pick interpolation problem in the class of the matrix-valued Stieltjes functions is derived as well.