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

Lev Aizenberg, Mark Elin, and David Shoikhet. "On the Rogosinski radius for holomorphic mappings and some of its applications." Studia Mathematica 168.2 (2005): 147-158. <http://eudml.org/doc/284898>.

@article{LevAizenberg2005,
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: $|∑_\{n=0\}^\{k\} aₙzⁿ| < 1$, |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.},
author = {Lev Aizenberg, Mark Elin, David Shoikhet},
journal = {Studia Mathematica},
keywords = {holomorphic mappings; power series extension; Bohr radius; Rogosinski radius; holomorphic generators; generalized complete Reinhardt domain; complex Banach spaces; Taylor series; Cauchy problem},
language = {eng},
number = {2},
pages = {147-158},
title = {On the Rogosinski radius for holomorphic mappings and some of its applications},
url = {http://eudml.org/doc/284898},
volume = {168},
year = {2005},
}

TY - JOUR
AU - Lev Aizenberg
AU - Mark Elin
AU - David Shoikhet
TI - On the Rogosinski radius for holomorphic mappings and some of its applications
JO - Studia Mathematica
PY - 2005
VL - 168
IS - 2
SP - 147
EP - 158
AB - 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.
LA - eng
KW - holomorphic mappings; power series extension; Bohr radius; Rogosinski radius; holomorphic generators; generalized complete Reinhardt domain; complex Banach spaces; Taylor series; Cauchy problem
UR - http://eudml.org/doc/284898
ER -