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

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.

Keywords

• Fourier transform
• fractional Fourier transform
• coupled fractional Fourier transform
• Schwartz space
• pseudo-differential operator