论全函数加权空间的强增长条件

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2024-08-08 DOI:10.1016/j.bulsci.2024.103490

Gerhard Schindl

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引用次数: 0

摘要

我们描述了具有快速递减增长的整个函数的加权类之间的包含关系，并研究了给定权重之间的强增长比较关系。在研究中，我们首先关注的是根据所谓关联权重函数定义的权重，其中权重（系统）是基于给定序列的。然后，通过使用所谓的关联权重序列，将抽象权重函数情况简化为权重序列情况。最后，我们比较了以所谓的扩张型权重系统和指数型权重系统定义的加权全函数空间。

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On strong growth conditions for weighted spaces of entire functions

We characterize the inclusion relations between weighted classes of entire functions with rapid decreasing growth and study strong growth comparison relations between given weights. In our considerations first we focus on weights defined in terms of the so-called associated weight function where the weight (system) is based on a given sequence. Then the abstract weight function case is reduced to the weight sequence setting by using the so-called associated weight sequence. Finally, we compare weighted entire function spaces defined in terms of so-called dilatation-type and exponential-type weight systems.

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