Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/162769 |
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| _version_ | 1832563814048989184 |
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| author | Mawardi Bahri Ryuichi Ashino Rémi Vaillancourt |
| author_facet | Mawardi Bahri Ryuichi Ashino Rémi Vaillancourt |
| author_sort | Mawardi Bahri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f8f2907619be431985433b09c3d41983 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f8f2907619be431985433b09c3d419832025-02-03T01:12:32ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/162769162769Convolution Theorems for Quaternion Fourier Transform: Properties and ApplicationsMawardi Bahri0Ryuichi Ashino1Rémi Vaillancourt2Department of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDivision of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, JapanDepartment of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, CanadaGeneral 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.http://dx.doi.org/10.1155/2013/162769 |
| spellingShingle | Mawardi Bahri Ryuichi Ashino Rémi Vaillancourt Convolution Theorems for Quaternion Fourier Transform: Properties and Applications Abstract and Applied Analysis |
| title | Convolution Theorems for Quaternion Fourier Transform: Properties and Applications |
| title_full | Convolution Theorems for Quaternion Fourier Transform: Properties and Applications |
| title_fullStr | Convolution Theorems for Quaternion Fourier Transform: Properties and Applications |
| title_full_unstemmed | Convolution Theorems for Quaternion Fourier Transform: Properties and Applications |
| title_short | Convolution Theorems for Quaternion Fourier Transform: Properties and Applications |
| title_sort | convolution theorems for quaternion fourier transform properties and applications |
| url | http://dx.doi.org/10.1155/2013/162769 |
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