由正则序列定义的 Carleman-Roumieu 超全纯类中渐近 Borel 映射的满射性
经典分析与常微分方程
2021-12-08 v2 复变函数
泛函分析
摘要
我们研究由 E. M. Dyn'kin 意义下的正则序列所定义的 Carleman-Roumieu 超全纯类中渐近 Borel 映射的满射性及其右逆的存在性。我们推广了 J. Schmets 与 M. Valdivia、V. Thilliez 以及作者先前的结果，并揭示了由 Thilliez 引入的与该序列相关联的一个指标所起的关键作用。相关技术涉及正则变分、积分变换，以及 A. Debrouwere 在半平面中的刻画结果——后者源于其对一般 Gelfand-Shilov 空间中矩映射满射性的研究。
引用
@article{arxiv.2007.06310,
title = {Surjectivity of the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences},
author = {Javier Jiménez-Garrido and Javier Sanz and Gerhard Schindl},
journal= {arXiv preprint arXiv:2007.06310},
year = {2021}
}
备注
18 pages. Some changes are related to an index shift in condition $(\beta_2)$, 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