# Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras
> Shah F.A.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_85137064061
Jurnal / Konferensi: Journal of Mathematics
Tahun terbit: 2022
DOI: https://doi.org/10.1155/2022/7848503
ISSN: 23144629
Kuartil SJR: Q3
Citations: 5

## Authors
- Shah F.A.

## Abstract
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.

## Keywords
- Shearlet
- Mathematics
- Clifford algebra
- Parseval's theorem
- Pure mathematics
- Fourier transform
- Pointwise
- Algebra over a field
- Mathematical analysis
- Fractional Fourier transform
- Fourier analysis
- Wavelet
- Artificial intelligence
- Computer science

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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