Surjectivity of the asymptotic Borel map in Carleman–Roumieu ultraholomorphic classes defined by regular sequences

We study the surjectivity of, and existence of right inverses for, asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences sense E. M. Dyn'kin. extend previous results J. Schmets Valdivia, V. Thilliez, authors, show prominent role played an index associated with sequence introduced Thilliez. The techniques involve variation, integral transforms characterization A. Debrouwere a half-plane, steming from his moment mapping general Gelfand-Shilov spaces.