Extension maps in ultradifferentiable and ultraholomorphic function spaces

The problem of the existence of extension maps from 0 to R in the setting o f the classical ultradifferentiable function spaces has been solved by Petz sche [9] by proving a generalization of the Borel and Mityagin theorems for C-infinity-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 f unctions, by first establishing a generalization to some nonclassical ultra differentiable function spaces.