The Borel-Ritt problem in Beurling ultraholomorphic classes

2020/06/29 by Debrouwere, Andreas
#30D60 #30E05 #46A63 #46M18 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2006.16175

Abstract

We give a complete solution to the Borel-Ritt problem in non-uniform spaces \mathscrA^-_(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 \mathscrA^-_(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].

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