The truncated Hamburger matrix moment problems in the nondegenerate and degenerate cases, and matrix continued fractions

AbstractThe present paper deals simultaneously with the nondegenerate and degenerate truncated Hamburger matrix moment problems in a unified way based on the use of the Schur algorithm involving matrix continued fractions. A full analysis of them together with a relative matrix moment problem on the real axis is given. With the help of the correspondence between the moment problem on the real axis and the Nevanlinna-Pick (NP) interpolation, the solutions of the nontangential NP interpolation in the Nevanlinna class are derived as an application