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

Lev Aizenberg, Mark Elin, David Shoikhet

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

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: | k ∑ n=0 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.

Original languageEnglish
Pages (from-to)147-158
Number of pages12
JournalStudia Mathematica
Volume168
Issue number2
DOIs
StatePublished - 2005

Keywords

  • Bohr radius
  • Cauchy problem
  • Holomorphic generators
  • Holomorphic mappings
  • Power series extension
  • Rogosinski radius

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