Continuation of holomorphic functions with growth conditions and some of its applications

Alexander V. Abanin, and Pham Trong Tien. "Continuation of holomorphic functions with growth conditions and some of its applications." Studia Mathematica 200.3 (2010): 279-295. <http://eudml.org/doc/285378>.

@article{AlexanderV2010,
abstract = {We prove a generalization of the well-known Hörmander theorem on continuation of holomorphic functions with growth conditions from complex planes in $ℂ^\{p\}$ into the whole $ℂ^\{p\}$. We apply this result to construct special families of entire functions playing an important role in convolution equations, interpolation and extension of infinitely differentiable functions from closed sets. These families, in their turn, are used to study optimal or canonical, in a certain sense, weight sequences defining inductive and projective type spaces of entire functions with O-growth conditions. Finally, we give a natural and complete description of multipliers for spaces given by canonical weight sequences.},
author = {Alexander V. Abanin, Pham Trong Tien},
journal = {Studia Mathematica},
keywords = {extension theorem},
language = {eng},
number = {3},
pages = {279-295},
title = {Continuation of holomorphic functions with growth conditions and some of its applications},
url = {http://eudml.org/doc/285378},
volume = {200},
year = {2010},
}

TY - JOUR
AU - Alexander V. Abanin
AU - Pham Trong Tien
TI - Continuation of holomorphic functions with growth conditions and some of its applications
JO - Studia Mathematica
PY - 2010
VL - 200
IS - 3
SP - 279
EP - 295
AB - We prove a generalization of the well-known Hörmander theorem on continuation of holomorphic functions with growth conditions from complex planes in $ℂ^{p}$ into the whole $ℂ^{p}$. We apply this result to construct special families of entire functions playing an important role in convolution equations, interpolation and extension of infinitely differentiable functions from closed sets. These families, in their turn, are used to study optimal or canonical, in a certain sense, weight sequences defining inductive and projective type spaces of entire functions with O-growth conditions. Finally, we give a natural and complete description of multipliers for spaces given by canonical weight sequences.
LA - eng
KW - extension theorem
UR - http://eudml.org/doc/285378
ER -