带三角权函数的多重卷积算子在Hartley积分变换中的应用

IF 0.7 3区数学 Q2 MATHEMATICS

Integral Transforms and Special Functions Pub Date : 2023-07-03 DOI:10.1080/10652469.2023.2230610

N. M. Khoa

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引用次数: 0

摘要

本文的主要目的是为Hartley积分变换建立一个新的带权函数的多卷积算子。之后，我们将把它应用于求解一些类型的积分方程和一个多卷积型的积分方程组。另一方面，我们研究了该多卷积的wastson型积分变换。建立了这些算子在空间上是酉的充分必要条件，并得到了它们的逆以共轭对称形式表示。进一步给出了上述算子的placherel型定理，证明了在范数下收敛于原函数的函数序列，并进一步证明了这些算子的有界性。

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 polyconvolution operator with a trigonometric weight function for the Hartley integral transforms and applications

The main aim of this work is to establish a new polyconvolution operator with the weight function for the Hartley integral transforms. After that, we will apply it to solve some classes of integral equations and a system of integral equations of polyconvolution type. On the other hand, we study the Wastson-type integral transform for this polyconvolution. We establish necessary and sufficient conditions for these operators to be unitary in the space and get their inverse represented in the conjugate symmetric form. Furthermore, we also formulate the Placherel-type theorem for the aforementioned operators, prove a sequence of functions that converges to the original function in the norm of , and further show the boundedness of these operators.

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来源期刊

Integral Transforms and Special Functions 数学-数学

CiteScore

2.20

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.