In the spirit of very recent articles by J. Bonet, W. Lusky and J. Taskinen we are studying the so-called solid hulls and cores of spaces of weighted entire functions when the weights are given in terms of associated weight functions coming from weight sequences. These sequences are required to satisfy certain (standard) growth and regularity properties which are frequently arising and used in the theory of ultradifferentiable and ultraholomorphic function classes (where also the associated weight function plays a prominent role). Thanks to this additional information we are able to see which growth behavior the so-called "Lusky-numbers", arising in the representations of the solid hulls and cores, have to satisfy resp. if such numbers can exist.

中文翻译：

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根据相关权重函数定义的加权整函数类的实体壳和核

本着 J. Bonet、W. Lusky 和 ​​J. Taskinen 最近文章的精神，我们正在研究加权全函数空间的所谓实体壳和核，当权重是根据来自权重的相关权重函数给出时序列。这些序列需要满足某些（标准）增长和规律性特性，这些特性在超微分和超全纯函数类理论中经常出现和使用（其中相关的权重函数也起着重要作用）。由于这些附加信息，我们能够看到在固体外壳和核心的表示中出现的所谓的“Lusky-numbers”必须满足哪些生长行为。如果这样的数字可以存在。