The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results have already been known for ultradifferentiable classes and it seems natural that they have ultraholomorphic counterparts. In order to have control on the opening of the sectors in the Riemann surface of the logarithm for which the extension theorems are valid we are introducing new mixed growth indices which are generalizing the known ones for weight sequences and functions. As it turns out, for the validity of mixed extension results the so-called order of quasianalyticity (introduced by the second author for weight sequences) is becoming important.

中文翻译：

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混合环境中的超全纯可拓定理

这项工作的目的是将 V. Thilliez 在权重序列设置中和作者在权重函数设置（Roumieu 类型）中的超全纯扩展定理推广到混合框架。对于超微分类，这种混合结果已经为人所知，并且它们具有超全纯对应物似乎很自然。为了控制扩展定理对其有效的对数的黎曼面上的扇区的开度，我们引入了新的混合增长指数，这些指数对权重序列和函数的已知指数进行了推广。事实证明，对于混合扩展结果的有效性，所谓的准分析阶（由第二作者为权重序列引入）变得越来越重要。