Open Access
2013 Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Mawardi Bahri, Ryuichi Ashino, Rémi Vaillancourt
Abstr. Appl. Anal. 2013: 1-10 (2013). DOI: 10.1155/2013/162769


General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.


Download Citation

Mawardi Bahri. Ryuichi Ashino. Rémi Vaillancourt. "Convolution Theorems for Quaternion Fourier Transform: Properties and Applications." Abstr. Appl. Anal. 2013 1 - 10, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1297.42015
MathSciNet: MR3124035
Digital Object Identifier: 10.1155/2013/162769

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
Back to Top