Weyl Sets in a Truncated Matricial Stieltjes Moment Problem

Abstract

Given a point w in the open upper complex half-plane $$\Pi _{\mathord {+}}$$ Π + , we describe the set of possible values $$F_\sigma \left( {w}\right) $$ F σ w of Stieltjes transforms $$F_\sigma \left( {z}\right) :=\int _{[\alpha ,\infty )}\left( {x-z}\right) ^{-1}\sigma \left( {\textrm{d}x}\right) $$ F σ z : = ∫ [ α , ∞ ) x - z - 1 σ d x , $$z\in \Pi _{\mathord {+}}$$ z ∈ Π + , corresponding to solutions $$\sigma $$ σ to a truncated matricial Stieltjes moment problem as intersection of two matrix balls.