用拉普拉斯变换刻画紧族

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2019-05-13 DOI:10.5186/aasfm.2020.4553

M. Krukowski

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引用次数: 5

摘要

1985年，Robert L. Pego用傅里叶变换描述了L^2(\real)$中的紧族。人们花了将近30年的时间才意识到Pego的结果可以在更广泛的局部紧化阿贝尔群(Gorka和Kostrzewa的作品)中得到证明。在当前的论文中，我们认为傅里叶变换并不是唯一有效表征紧族的积分变换，并建议拉普拉斯变换作为一种可能的替代方法。

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Characterizing compact families via the Laplace transform

In 1985, Robert L. Pego characterized compact families in $L^2(\reals)$ in terms of the Fourier transform. It took nearly 30 years to realize that Pego's result can be proved in a wider setting of locally compact abelian groups (works of Gorka and Kostrzewa). In the current paper, we argue that the Fourier transform is not the only integral transform that is efficient in characterizing compact families and suggest the Laplace transform as a possible alternative.

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.