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- Title
Convolution Theorems for Quaternion Fourier Transform: Properties and Applications.
- Authors
Bahri, Mawardi; Ashino, Ryuichi; Vaillancourt, Rémi
- Abstract
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.
- Subjects
MATHEMATICAL convolutions; QUATERNIONS; FOURIER transforms; HEAT equation; HYPOELLIPTIC operators
- Publication
Abstract & Applied Analysis, 2013, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2013/162769