通过连续性模量实现哈特里变换的增长特性

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-09-07 DOI:10.1007/s11868-024-00628-9

Nurbek Kakharman, Niyaz Tokmagambetov

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引用次数: 0

摘要

本研究探讨了函数的连续性模量与其哈特利变换之间的关系。我们通过推导重要结果，如黎曼-莱伯斯格（Riemann-Lebesgue）lemma、帕赛瓦尔（Parseval）定理，以及欧几里得空间和环空间中哈特利变换的豪斯多夫-杨不等式，来探索这种联系。利用平移算子，我们得到了哈特利变换的蒂奇马什定理。此外，我们还将分析扩展到了环上的哈特里级数。

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Growth properties of Hartley transform via moduli of continuity

This study investigates the relationship between the moduli of continuity of a function and its Hartley transform. We explore this connection by deriving significant results such as the Riemann–Lebesgue lemma, Parseval’s theorem, and the Hausdorff–Young inequality for the Hartley transform in both the Euclidean space and torus. Using a translation operator, we obtain an analog of Titchmarsh’s theorem for the Hartley transform. In addition, we extend our analysis to the Hartley series on the torus.

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来源期刊

Journal of Pseudo-Differential Operators and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.20

自引率

9.10%

发文量

期刊介绍： The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.