Optimal flat functions in Carleman-Roumieu ultraholomorphic classes in sectors

Abstract

A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, whenever optimal flat functions are available in Carleman-Roumieu ultraholomorphic classes, defined on sectors and in terms of regular weight sequences in the sense of Dyn'kin. For a family of regular sequences, including the well-known q-Gevrey case, we construct such optimal flat functions in arbitrary sectors of the Riemann surface of the logarithm.