The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
@article{bwmeta1.element.bwnjournal-article-smv143i3p221bwm,
author = {Jean Schmets and Manuel Valdivia},
title = {Extension maps in ultradifferentiable and ultraholomorphic function spaces},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {221-250},
zbl = {0972.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv143i3p221bwm}
}
Schmets, Jean; Valdivia, Manuel. Extension maps in ultradifferentiable and ultraholomorphic function spaces. Studia Mathematica, Tome 141 (2000) pp. 221-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv143i3p221bwm/
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