Journal
ABSTRACT AND APPLIED ANALYSIS
Volume -, Issue -, Pages -Publisher
HINDAWI LTD
DOI: 10.1155/2013/162769
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Funding
- Hibah Penelitian Kompetisi Internal Tahun from the Hasanuddin University, Indonesia [110/UN4-.42/LK.26/SP-UH/2013]
- JSPS.KAKENHI of Japan [22540130, 25400202]
- NSERC of Canada
- Grants-in-Aid for Scientific Research [23540135, 22540130] Funding Source: KAKEN
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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.
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