The talk will be devoted to the study of Taylor coefficients in spaces of smooth functions that lie between real analytic functions and infinitely differentiable functions, such as Denjoy-Carleman spaces. It was known already to Borel that in some of these spaces, a description of the set of Taylor coefficients cannot be given in metric terms.

I will give a description based on moment summation methods, extending upon the classical results of Beurling and Nevanlinna.