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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-4,
author = {Taib Belghiti},
title = {Holomorphic series expansion of functions of Carleman type},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {219-224},
zbl = {1067.30093},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-4}
}
Taib Belghiti. Holomorphic series expansion of functions of Carleman type. Annales Polonici Mathematici, Tome 83 (2004) pp. 219-224. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-4/