From the Potapov to the Krein–Nudel’man representation of the resolvent matrix of the truncated Hausdorff matrix moment problem

Abstract

In their book The Markov Moment Problem and Extremal Problems, published in 1977, M. G. Krein and A. A. Nudel’man presented a complete solution of the truncated Hausdorff moment problem via orthogonal polynomials on a finite interval [a, b]. By using the Potapov schema the matrix version of this moment problem was studied by the author, Yu. M. Dyukarev, B. Fritzsche and B. Kirstein. In the present work, we obtain the matrix generalisation of the above-mentioned Krein–Nudel’man representation. We also obtain explicit relations between four families of orthogonal matrix polynomials on [a, b] and their second kind polynomials, which are associated with the matrix version of the truncated Hausdorff moment problem.