On Degenerate Hamburger Moment Problem and Extensions of Positive Semidefinite Hankel Block Matrices

In this paper we consider two related objects: singular positive semidefinite Hankel block–matrices and associated degenerate truncated matrix Hamburger moment problems. The description of all solutions of a degenerate matrix Hamburger moment problem is given in terms of a linear fractional transformation. The case of interest is the Hamburger moment problem whose Hankel block–matrix admits a positive semidefinite Hankel extension. This is the corrected version of the original paper [2]. The work was inspired by V. Dubovoj’s paper [4] containing the first systematic study of degenerate matricial interpolation problems. Another sourse of inspiration must have been the paper by R. Curto and L. Fialkow [3] but I was not aware of it then. The original paper contained several erratae and the author is very grateful to A. Ben-Artzi and H. Woerdeman for indicating them. A short proof in Section 5 fixes these incorrectnesses. The remaining four sections are mostly the same as in [2].