The Borel–Ritt Problem in Beurling Ultraholomorphic Classes

We give a complete solution to the Borel–Ritt problem in non-uniform spaces $${\mathscr {A}}^-_{(M)}(S)$$ of ultraholomorphic functions Beurling type, where S is an unbounded sector Riemann surface logarithm and M strongly regular weight sequence. Namely, we characterize surjectivity existence continuous linear right inverse asymptotic Borel map on terms aperture sequence M. Our work improves previous results by Thilliez (Results Math 44:169–188, 2003) Schmets Valdivia (Stud 143:221–250, 2000).