TW 290
A. Bultheel and P. Van gucht
Boundary asymptotics for orthogonal rational functions on the unit circle
Abstract
Let w(θ) be a positive weight function
on the unit circle of the complex plane.
For a sequence of points
{αk}k=1∞
included in a compact subset of the unit disk,
we consider the orthogonal rational functions
φn
that are obtained by orthogonalization of the sequence
{1,z/π1,z2/π2,...} where
πk(z)=
∏j=1k
(1-α*jz),
with respect to the inner product
We discuss in this paper the behaviour of φ
n(z) for
|z|=1 and n → ∞
under certain conditions.
The main condition on the weight is that it satisfies a
Lipschitz-Dini condition and that it is bounded away from zero.
This generalizes a theorem given by Szegö in the polynomial case, that is when
all α
k=0.
report.pdf /
mailto: P. Van gucht
