Bulletin of Computational Applied Mathematics (Bull CompAMa)
One-dimensional Quaternion Fourier Transform and Some Applications
Eusebio Ariza García, Claudia Jiménez Heredia, Carlos Chipantiza
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.