广义多重计量序列的成就集

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-04-13 DOI:10.1007/s00025-024-02158-8

Dmytro Karvatskyi, Aniceto Murillo, Antonio Viruel

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引用次数: 0

摘要

我们研究广义多重几何数列\(k_1f(x)+k_2f(x)+\dots +k_mf(x)+\dots + k_1f(x^n)+\dots +k_mf(x^n)+\dots ,\)的所有可能子集的拓扑结构，其中\(k_1, k_2, \dots , k_m\)是固定的正实数，f沿着单位区间上的某类非负函数运行。我们检测了这个区间的特定区域，对于这些区域，这个成就集分别是一个紧凑区间、一个康托集和一个康托瓦尔。

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The Achievement Set of Generalized Multigeometric Sequences

We study the topology of all possible subsums of the generalized multigeometric series \(k_1f(x)+k_2f(x)+\dots +k_mf(x)+\dots + k_1f(x^n)+\dots +k_mf(x^n)+\dots ,\) where \(k_1, k_2, \dots , k_m\) are fixed positive real numbers and f runs along a certain class of non-negative functions on the unit interval. We detect particular regions of this interval for which this achievement set is, respectively, a compact interval, a Cantor set and a Cantorval.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.