Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras
The shearlet transform is a promising and powerful time-frequency tool for analyzing nonstationary signals. In this article, we introduce a novel integral transform coined as the Clifford-valued shearlet transform on Cl(p,q) algebras which is designed to represent Clifford-valued signals at differen...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7848503 |
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| author | Firdous A. Shah Aajaz A. Teali Mawardi Bahri |
| author_facet | Firdous A. Shah Aajaz A. Teali Mawardi Bahri |
| author_sort | Firdous A. Shah |
| collection | DOAJ |
| description | The shearlet transform is a promising and powerful time-frequency tool for analyzing nonstationary signals. In this article, we introduce a novel integral transform coined as the Clifford-valued shearlet transform on Cl(p,q) algebras which is designed to represent Clifford-valued signals at different scales, locations, and orientations. We investigated the fundamental properties of the Clifford-valued shearlet transform including Parseval’s formula, isometry, inversion formula, and characterization of range using the machinery of Clifford Fourier transforms. Moreover, we derived the pointwise convergence and homogeneous approximation properties for the proposed transform. We culminated our investigation by deriving several uncertainty principles such as the Heisenberg–Pauli–Weyl uncertainty inequality, Pitt’s inequality, and logarithmic and local-type uncertainty inequalities for the Clifford-valued shearlet transform. |
| format | Article |
| id | doaj-art-a0f9fdc3e7e7429e8e0b4aa28203257b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a0f9fdc3e7e7429e8e0b4aa28203257b2025-02-03T01:22:52ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/7848503Clifford-Valued Shearlet Transforms on Cl(P,Q)-AlgebrasFirdous A. Shah0Aajaz A. Teali1Mawardi Bahri2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThe shearlet transform is a promising and powerful time-frequency tool for analyzing nonstationary signals. In this article, we introduce a novel integral transform coined as the Clifford-valued shearlet transform on Cl(p,q) algebras which is designed to represent Clifford-valued signals at different scales, locations, and orientations. We investigated the fundamental properties of the Clifford-valued shearlet transform including Parseval’s formula, isometry, inversion formula, and characterization of range using the machinery of Clifford Fourier transforms. Moreover, we derived the pointwise convergence and homogeneous approximation properties for the proposed transform. We culminated our investigation by deriving several uncertainty principles such as the Heisenberg–Pauli–Weyl uncertainty inequality, Pitt’s inequality, and logarithmic and local-type uncertainty inequalities for the Clifford-valued shearlet transform.http://dx.doi.org/10.1155/2022/7848503 |
| spellingShingle | Firdous A. Shah Aajaz A. Teali Mawardi Bahri Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras Journal of Mathematics |
| title | Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras |
| title_full | Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras |
| title_fullStr | Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras |
| title_full_unstemmed | Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras |
| title_short | Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras |
| title_sort | clifford valued shearlet transforms on cl p q algebras |
| url | http://dx.doi.org/10.1155/2022/7848503 |
| work_keys_str_mv | AT firdousashah cliffordvaluedshearlettransformsonclpqalgebras AT aajazateali cliffordvaluedshearlettransformsonclpqalgebras AT mawardibahri cliffordvaluedshearlettransformsonclpqalgebras |