Weyl Sets in a Non-degenerate Truncated Matricial Hausdorff Moment Problem

Abstract

Given a point w in the upper half-plane \(\Pi _{\mathord {+}}\), we describe the set of all possible values F(w) of transforms \(F(z)\,{:=}\,\int _{[\alpha ,\beta ]}(x-z)^{-1}\sigma (\textrm{d}x)\), \(z\in \Pi _{\mathord {+}}\), corresponding to solutions \(\sigma \) to a (non-degenerate) truncated matricial Hausdorff moment problem. This set turns out to be the intersection of two matrix balls the parameters of which are explicitly constructed from the given data.