A discussion on non-archimedean pseudo-differential operator related with the coupled fractional Fourier transform

Abstract

We introduce and study a new class of non-archimedean pseudo-differential operator connected to coupled fractional Fourier transform. Motivated by Fractional Fourier transform and non-archimedean pseudo-differential connected to negative definite functions discussed by Shekhar and Agrawal [1,2], we discuss non-archimedean pseudo-differential operator connected to coupled fractional Fourier transform. This provides a new framework parallel to the classical Fourier non-archimedean pseudo-differential calculus, but in a non-archimedean analysis and global setting.