论文标题
Borel-Ritt的问题
The Borel-Ritt problem in Beurling ultraholomorphic classes
论文作者
论文摘要
我们为非均匀空间中的Borel-Ritt问题提供了完整的解决方案，$ \ Mathscr {a}^-_ {（M）}（M）}（s）$ beurling类型的Ultraholomorphic函数，其中$ s $是Aboolegarithmant and $ m $ $ $ $ $ $ $ $ $ $ $ $的无界领域，是一个强度常规的序列。也就是说，我们表征了$ \ Mathscr {a}^-_ {（m）}（M）}（M）} $在扇区$ $ s $和权重序列$ m $上的渐近线性直接右线性直接的倒数右线。我们的工作改善了Thilliez [10]和Schmets和Valdivia [9]的先前结果。
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].
