Inverse Laplace Transform for Bi-Complex Variables

TL;DR

This paper explores the extension of the inverse Laplace transform to bicomplex variables, using idempotent representation to analyze convergence and function projections in bicomplex analysis.

Contribution

It introduces a bicomplex inverse Laplace transform framework utilizing idempotent decomposition, extending classical methods to bicomplex-valued functions.

Findings

Established conditions for the existence of bicomplex inverse Laplace transform.

Demonstrated the use of idempotent representation for function analysis in bicomplex space.

Extended classical Laplace transform techniques to bicomplex variables.

Abstract

In this paper we examine the existence of bicomplexied inverse Laplacetransform as an extension of its complexied inverse version within theregion of convergence of bicomplex Laplace transform. In this course weuse the idempotent representation of bicomplex-valued functions as pro-jections on the auxiliary complex spaces of the components of bicomplexnumbers along two orthogonal,idempotent hyperbolic directions.