Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse

Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space epsilon((omega)) (R) of (omega)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (omega)-ultradifferential operators which admit a continuous linear right inverse on epsilon((omega)) [a, b] for each compact interval [a, b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on epsilon((omega)) (R).