The Borel-Ritt problem in Beurling ultraholomorphic classes

Abstract

We give a complete solution to the Borel-Ritt problem in non-uniform spaces ${\mathcal{A}}_{(M)}^{-}(S)$ of ultraholomorphic functions of Beurling type, where $S$ is an unbounded sector of the Riemann surface of the logarithm and $M$ is a strongly regular weight sequence. Namely, we characterize the surjectivity and the existence of a continuous linear right inverse of the asymptotic Borel map on ${\mathcal{A}}_{(M)}^{-}(S)$ in terms of the aperture of the sector $S$ and the weight sequence $M$. Our work improves previous results by Thilliez [10] and Schmets and Valdivia [9].

13 pages; updated version