关于Henstock-Kurzweil傅立叶变换的推广

Journal of classical analysis Pub Date : 2022-02-21 DOI:10.7153/jca-2022-20-09

S. Mahanta, S. Ray

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引用次数: 2

摘要

本文在无界区间上定义了一个广义积分，称为拉普拉斯积分，并讨论了它的一些性质，包括在积分符号下微分的充要条件。还证明了该积分比Henstock-Kurzweil积分更一般。最后，利用拉普拉斯积分定义了傅立叶变换，并建立了其众所周知的性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the generalisation of Henstock-Kurzweil Fourier transform

In this paper, a generalised integral called the Laplace integral is defined on unbounded intervals, and some of its properties, including necessary and sufficient condition for differentiating under the integral sign, are discussed. It is also shown that this integral is more general than the Henstock-Kurzweil integral. Finally, the Fourier transform is defined using the Laplace integral, and its well-known properties are established.

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来源期刊

Journal of classical analysis

CiteScore

1.00

自引率

0.00%

发文量