Extension maps in ultradifferentiable and ultraholomorphic function spaces
Volume 143 / 2000
Studia Mathematica 143 (2000), 221-250
DOI: 10.4064/sm-143-3-221-250
Abstract
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 $C^{∞}$-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.
