Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras

�e 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 Cli�ord-valued shearlet transform on Cl(p,q) algebras which is designed to represent Cli�ord-valued signals at di�erent scales, locations, and orientations. We investigated the fundamental properties of the Cli�ord-valued shearlet transform including Parseval’s formula, isometry, inversion formula, and characterization of range using the machinery of Cli�ord 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
Cli�ord-valued shearlet transform