Abstract:
Recently, we presented a general procedure 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. In this talk, we are going to present a new weaker condition for the sequence which allows us to proof the surjectivity of the Borel map in the same classes following a slightly modified technique. Moreover, we show new results concerning the surjectivity of the Borel map in Beurling ultraholomorphic classes using this new condition and a suitable adaptation of results by V. Thilliez and J. Chaumat and A.M. Chollet.