Author:
Heide Max,Fritzsche Bernd,Kirstein Bernd,Mädler Conrad
Abstract
AbstractGiven a point w in the upper half-plane $$\Pi _{\mathord {+}}$$
Π
+
, 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
)
:
=
∫
[
α
,
β
]
(
x
-
z
)
-
1
σ
(
d
x
)
, $$z\in \Pi _{\mathord {+}}$$
z
∈
Π
+
, corresponding to solutions $$\sigma $$
σ
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.
Publisher
Springer Science and Business Media LLC