Beurling超全纯类中的Borel-Ritt问题
The Borel-Ritt problem in Beurling ultraholomorphic classes
摘要：
本文给出了Beurling型超全纯函数的非一致空间$\mathscr{A}^-_{(M)}(S)$中Borel-Ritt问题的完全解，其中$S$是对数Riemann曲面的无界扇区，$M$是强正则权序列.即利用扇区$S$的孔径和权序列$M$刻画了$\mathscr{A}^-_{(M)}(S)$上渐近Borel映射的满射性和连续线性右逆的存在性.我们的工作改进了Thilliez [10]和Schmets和Valdivia [9]的结果。
英文摘要：
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].
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