ON THE RANGE OF CONVOLUTION-OPERATORS ON NON-QUASIANALYTIC ULTRADIFFERENTIABLE FUNCTIONS

Let epsilon((omega))(Omega) denote the non-quasianalytic class of Beur ling type on an open set Omega in R-n. For mu is an element of epsilon '((omega))(R-n) the surjectivity of the convolution operator T mu : ep silon((omega))(Omega(1)) --> epsilon((omega))(Omega(2)) is characteriz ed by various conditions, e.g. in terms of a convexity property of the pair (Omega(1) Omega(2)) and the existence of a fundamental solution for mu or equivalently by a slowly decreasing condition for the Fourie r-Laplace transform of mu. Similar conditions characterize the surject ivity of a convolution operator S-mu : D'({omega})(Omega(1)) --> D'({o mega })(Omega(2)) between ultradistributions of Roumieu type whenever mu is an element of epsilon'({omega})(R-n). These results extend class ical work of Hormander on convolution operators between spaces of C-in finity-functions and more recent one of Cioranescu and Braun, Meise an d Vogt.