Holomorphic series expansion of functions of Carleman type

Taib Belghiti. "Holomorphic series expansion of functions of Carleman type." Annales Polonici Mathematici 84.3 (2004): 219-224. <http://eudml.org/doc/280823>.

@article{TaibBelghiti2004,
abstract = {Let f be a holomorphic function of Carleman type in a bounded convex domain D of the plane. We show that f can be expanded in a series f = ∑ₙfₙ, where fₙ is a holomorphic function in Dₙ satisfying $sup_\{z∈Dₙ\}|fₙ(z)| ≤ Cϱⁿ$ for some constants C > 0 and 0 < ϱ < 1, and where (Dₙ)ₙ is a suitably chosen sequence of decreasing neighborhoods of the closure of D. Conversely, if f admits such an expansion then f is of Carleman type. The decrease of the sequence Dₙ characterizes the smoothness of f.},
author = {Taib Belghiti},
journal = {Annales Polonici Mathematici},
keywords = {Carleman class; holomorphic expansion},
language = {eng},
number = {3},
pages = {219-224},
title = {Holomorphic series expansion of functions of Carleman type},
url = {http://eudml.org/doc/280823},
volume = {84},
year = {2004},
}

TY - JOUR
AU - Taib Belghiti
TI - Holomorphic series expansion of functions of Carleman type
JO - Annales Polonici Mathematici
PY - 2004
VL - 84
IS - 3
SP - 219
EP - 224
AB - Let f be a holomorphic function of Carleman type in a bounded convex domain D of the plane. We show that f can be expanded in a series f = ∑ₙfₙ, where fₙ is a holomorphic function in Dₙ satisfying $sup_{z∈Dₙ}|fₙ(z)| ≤ Cϱⁿ$ for some constants C > 0 and 0 < ϱ < 1, and where (Dₙ)ₙ is a suitably chosen sequence of decreasing neighborhoods of the closure of D. Conversely, if f admits such an expansion then f is of Carleman type. The decrease of the sequence Dₙ characterizes the smoothness of f.
LA - eng
KW - Carleman class; holomorphic expansion
UR - http://eudml.org/doc/280823
ER -