On the Rogosinski radius for holomorphic mappings and some of its applications

• Autorzy: Lev Aizenberg , Mark Elin , David Shoikhet
• Języki publikacji: EN

Abstrakty

EN

The well known theorem of Rogosinski asserts that if the modulus of the sum of a power series is less than 1 in the open unit disk: $|∑_{n=0}^{∞} aₙzⁿ| < 1$, |z| < 1, then all its partial sums are less than 1 in the disk of radius 1/2:
$|∑_{n=0}^{k} aₙzⁿ| < 1$, |z| < 1/2,
and this radius is sharp. We present a generalization of this theorem to holomorphic mappings of the open unit ball into an arbitrary convex domain. Other multidimensional analogs of Rogosinski's theorem as well as some applications to dynamical systems are considered.

Kategorie tematyczne

• 32A05: Power series, series of functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 168
• Numer: 2
• Strony: 147-158

Daty

wydano

2005

Twórcy

autor

Lev Aizenberg

• Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel

autor

Mark Elin

• Department of Mathematics, ORT Braude College, 21982 Karmiel, Israel

autor

David Shoikhet

• Department of Mathematics, ORT Braude College, 21982 Karmiel, Israel

Identyfikatory

DOI

10.4064/sm168-2-5