One-dimensional Quaternion Fourier Transform and Some Applications

Abstract

The Fourier transform is a very useful tool in many areas. This transform has been defined in many contexts, as complex numbers, quaternions, and Clifford algebras. This paper deals with a one$-$dimensional Fourier Transform defined for quaternion-valued functions. Some of its fundamental properties are proved, particularly, the inversion formula, which will be use to prove another important inversion formula for a two-dimensional quaternion Fourier transform. Using this Fourier transform, we also solve a partial differential equation.

Keywords

• quaternions
• one-dimensional quaternion fourier transform
• inversion formula