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

Given a point w in the upper half-plane \(\Pi _{\mathord {+}}\) ${\mathrm{\Pi }}_{+}$ , we describe the set of all possible values F(w) of transforms \(F(z)\,{:=}\,\int _{[\alpha ,\beta ]}(x-z)^{-1}\sigma (\textrm{d}x)\) $F(z):={\int }_{[\alpha ,\beta ]}{(x-z)}^{-1}\sigma (\text{d}x)$ , \(z\in \Pi _{\mathord {+}}\) $z\in {\mathrm{\Pi }}_{+}$ , corresponding to solutions \(\sigma \) $\sigma$ 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.