Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated Convolution
The primary focus of the present study is to analyse the Clifford-valued functions by introducing the notion of a two-sided Clifford-valued special affine Fourier transform in L2(Rn,Cl0,n). Firstly we propose the novel definition of the Clifford-valued special affine Fourier transform and derive its...
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| Format: | Article |
| Language: | English |
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Mathyze Publishers
2024-07-01
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| Series: | Pan-American Journal of Mathematics |
| Online Access: | https://mathyze.com/index.php/pajm/article/view/194 |
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| author | Shahbaz Rafiq M. Younus Bhat |
| author_facet | Shahbaz Rafiq M. Younus Bhat |
| author_sort | Shahbaz Rafiq |
| collection | DOAJ |
| description | The primary focus of the present study is to analyse the Clifford-valued functions by introducing the notion of a two-sided Clifford-valued special affine Fourier transform in L2(Rn,Cl0,n). Firstly we propose the novel definition of the Clifford-valued special affine Fourier transform and derive its fundamental properties which include inversion formula, translation covariance, scaling covariance and Plancherel formula. Subsequently we introduce the boundedness, continuity and differentiation theorems for the proposed transform. Finally we culminate our investigation by deriving the convolution for this newly proposed transform. |
| format | Article |
| id | doaj-art-32e5afbaba1442a3aefe2c235c9b96d2 |
| institution | OA Journals |
| issn | 2832-4293 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Mathyze Publishers |
| record_format | Article |
| series | Pan-American Journal of Mathematics |
| spelling | doaj-art-32e5afbaba1442a3aefe2c235c9b96d22025-08-20T02:34:59ZengMathyze PublishersPan-American Journal of Mathematics2832-42932024-07-013010.28919/cpr-pajm/3-1855Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated ConvolutionShahbaz Rafiq0M. Younus Bhat1Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, India.Department of Mathematical Sciences, Islamic University of Science and Technology KashmirThe primary focus of the present study is to analyse the Clifford-valued functions by introducing the notion of a two-sided Clifford-valued special affine Fourier transform in L2(Rn,Cl0,n). Firstly we propose the novel definition of the Clifford-valued special affine Fourier transform and derive its fundamental properties which include inversion formula, translation covariance, scaling covariance and Plancherel formula. Subsequently we introduce the boundedness, continuity and differentiation theorems for the proposed transform. Finally we culminate our investigation by deriving the convolution for this newly proposed transform.https://mathyze.com/index.php/pajm/article/view/194 |
| spellingShingle | Shahbaz Rafiq M. Younus Bhat Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated Convolution Pan-American Journal of Mathematics |
| title | Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated Convolution |
| title_full | Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated Convolution |
| title_fullStr | Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated Convolution |
| title_full_unstemmed | Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated Convolution |
| title_short | Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated Convolution |
| title_sort | two sided clifford valued special affine fourier transform properties and associated convolution |
| url | https://mathyze.com/index.php/pajm/article/view/194 |
| work_keys_str_mv | AT shahbazrafiq twosidedcliffordvaluedspecialaffinefouriertransformpropertiesandassociatedconvolution AT myounusbhat twosidedcliffordvaluedspecialaffinefouriertransformpropertiesandassociatedconvolution |