Fourier transform for functions of bicomplex variables

TL;DR

This paper explores the Fourier transform of functions of bicomplex variables, focusing on convergence regions and properties using idempotent projections onto complex planes.

Contribution

It introduces a bicomplex Fourier transform framework, analyzing its convergence and fundamental properties through idempotent decomposition.

Findings

Identifies convergence regions for bicomplex Fourier transforms

Establishes basic properties of the bicomplex Fourier transform

Uses idempotent projections to analyze bicomplex functions

Abstract

This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this bicomplex version of Fourier transform are examined.