The Borel-Ritt problem in Beurling ultraholomorphic classes

15 Nov 2020  ·  Debrouwere Andreas ·

We give a complete solution to the Borel-Ritt problem in non-uniform spaces $\mathscr{A}^-_{(M)}(S)$ 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 $\mathscr{A}^-_{(M)}(S)$ 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]. read more

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Functional Analysis