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• # Artykuł - szczegóły

## Studia Mathematica

2005 | 168 | 2 | 147-158

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

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.

147-158

wydano
2005

### Twórcy

autor
• Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
autor
• Department of Mathematics, ORT Braude College, 21982 Karmiel, Israel
autor
• Department of Mathematics, ORT Braude College, 21982 Karmiel, Israel