Anzeige
Erschienen in:
2012 | OriginalPaper | Buchkapitel
Growth Behavior and Zero Distribution of Maximally Convergent Rational Approximants
verfasst von : Hans-Peter Blatt, René Grothmann, Ralitza K. Kovacheva
Erschienen in: Approximation Theory XIII: San Antonio 2010
Verlag: Springer New York
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Given a compact set
E
in
$$\mathbb{C}$$
and a function
f
holomorphic on
E
, we investigate the distribution of zeros of rational uniform approximants
$$\{{r}_{n,{m}_{n}}\}$$
with numerator degree≤
n
and denominator degree≤
m
n
, where
$${m}_{n} = o(n/\log n)$$
as
n
→
∞
. We obtain a Jentzsch–Szegő type result, i.e., the zero distribution converges weakly to the equilibrium distribution of the maximal Green domain
E
ρ(
f
)
of meromorphy of
f
if
f
has a singularity of multivalued character on the boundary
∂E
ρ(
f
)
. Further, we show that any singular point of
f
on the boundary
∂E
ρ(
f
)
, that is not a pole, is a limit point of zeros of the sequence
$$\{{r}_{n,{m}_{n}}\}$$
.