Boundedness of pseudo-differential operators via coupled fractional Fourier transform

被引：1

作者：

Das, Shraban ^{[1
]}

Mahato, Kanailal ^{[2
]}

Das, Sourav ^{[1
]}

机构：

[1] Natl Inst Technol Jamshedpur, Dept Math, Jamshedpur, Jharkhand, India

[2] Banaras Hindu Univ, Inst Sci, Dept Math, Varanasi, India

来源：

APPLICABLE ANALYSIS | 2025年 / 104卷 / 04期

关键词：

Fourier transform; fractional Fourier transform; coupled fractional Fourier transform; Sobolev space; pseudo-differential operator; PRODUCT; WIGNER; ORDER;

D O I：

10.1080/00036811.2024.2378209

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we obtained some fruitful results of the coupled fractional Fourier transform and its kernel. We defined pseudo-differential operators related to coupled fractional Fourier transform on Schwartz spaces and it is shown that their composition is again a pseudo-differential operator. It made further discussion on the composition of two pseudo-differential operators on Sobolev spaces and derived certain norm inequalities on it. Further, we have successfully applied some of the results of the coupled fractional Fourier transform to investigate the solution of nth-order linear non-homogeneous partial differential equation and wave equation. Lastly, we present some examples involving graphs and tables to illustrate the validity of our theoretical findings.

引用

页码：663 / 681

页数：19

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