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arXiv 2007.06310math.CAmath.CVmath.FA
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由正则序列定义的Carleman-Roumieu超全纯类中渐近Borel映射的满射性

Surjectivity of the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences

Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl

备注：
18 pages. Some changes are related to an index shift in condition $(β_2)$, property (9) and the proof of Proposition 4.4. The example proving that (vii) does not imply (vi) in that Proposition has been changed. New proof, avoiding the use of condition (dc), for the implication from (i) to (ii) in Theorem 4.5. Some new comments added and some misprints corrected
发表信息：
Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, no. 115, art. no. 181, 2021
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摘要：

我们研究了由E意义下的正则序列定义的Carleman-Roumieu超全纯类中的渐近Borel映射的满射性及其右逆的存在性。M.很好推广了J. Schmets和M. Valdivia，作者V. Thilliez和作者，并展示了与序列相关并由Thilliez引入的索引所发挥的突出作用。这些技术包括正则变分、积分变换和A. Debrouwere在一个半平面，从他的研究满射的时刻映射一般Gelfand-Shilov空间。

英文摘要：

We study the surjectivity of, and the existence of right inverses for, the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences in the sense of E. M. Dyn'kin. We extend previous results by J. Schmets and M. Valdivia, by V. Thilliez, and by the authors, and show the prominent role played by an index associated with the sequence and introduced by Thilliez. The techniques involve regular variation, integral transforms and characterization results of A. Debrouwere in a half-plane, steming from his study of the surjectivity of the moment mapping in general Gelfand-Shilov spaces.

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