Let
A Γ
-inner function is a holomorphic map
h from the unit disc
D to Γ whose boundary values at almost all points of the unit circle
T belong to the distinguished boundary
bΓ of Γ. A rational Γ-inner function
h induces a continuous map
h|T from
T to
b Γ. The latter set is topologically a Möbius band and so has fundamental group
Z. The
degree of
h is defined to be the topological degree of
h|T. In a previous paper the authors showed that if
h=(s,p) is a rational Γ-inner function of degree
n then
s2−4p has exactly
n zeros in the closed unit disc
D−, counted with an appropriate notion of multiplicity. In this paper, with the aid of a solution of an interpolation problem for finite Blaschke
products, we explicitly construct the rational Γ-inner functions of degree
n with the
n zeros of
s2−4p prescribed.
