Inverse Fourier Transform for Bi-Complex Variables

TL;DR

This paper explores the extension of the inverse Fourier transform to bicomplex variables, utilizing idempotent representation to analyze convergence and properties within bicomplex analysis.

Contribution

It introduces the bicomplexified inverse Fourier transform and demonstrates its existence using idempotent decomposition in bicomplex analysis.

Findings

Existence of bicomplex inverse Fourier transform established

Utilizes idempotent representation for analysis

Extends classical Fourier analysis to bicomplex domain

Abstract

In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent representation of bicomplex-valued functions as projections on the auxiliary complex spaces of the components of bicomplex numbers along two orthogonal,idempotent hyperbolic directions.