Characterization of Pseudo-Differential Operators Associated with the Coupled Fractional Fourier Transform-Reference-Cited by-同舟云学术

Characterization of Pseudo-Differential Operators Associated with the Coupled Fractional Fourier Transform

Published:2024-04-28 Issue:5 Volume:13 Page:296
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Das Shraban¹,Mahato Kanailal²,Zayed Ahmed I.³

Affiliation:

1. Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, India

2. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India

3. Department of Mathematical Sciences, Depaul University, Chicago, IL 60614, USA

Abstract

The main aim of this article is to derive certain continuity and boundedness properties of the coupled fractional Fourier transform on Schwartz-like spaces. We extend the domain of the coupled fractional Fourier transform to the space of tempered distributions and then study the mapping properties of pseudo-differential operators associated with the coupled fractional Fourier transform on a Schwartz-like space. We conclude the article by applying some of the results to obtain an analytical solution of a generalized heat equation.

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/5/296/pdf

Reference26 articles.

1. The fractional order Fourier and its application to quantum mechanics;Namias;J. Inst. Math. Appl.,1980

2. On Namias’s fractional Fourier transforms;McBride;IMA J. Appl. Math.,1987

3. Namias’ fractional Fourier transform on L2 and applications to quantum mechanics;Kerr;J. Math. Anal. Appl.,1988

4. The angular Fourier transform in optical propagation problems;Alieva;J. Mod. Opt.,1994

5. The fractional Fourier transform and time-frequency representations;Almeida;IEEE Trans. Signal. Process.,1994