This paper deals with the construction of \(n=3 \text{ mod } 4\) Clifford algebra \(Cl_{n,0}\)-valued admissible shearlet transform using the shearlet group \((\mathbb {R}^* < imes \mathbb {R}^{n-1}) < imes \mathbb {R}^n\), a subgroup of affine group of \({\mathbb {R}}^n\). The admissibility conditions for a nonzero Clifford valued square integrable function have been obtained. Various properties such as reconstruction formula, orthogonality relation, isometry and reproducing kernel have been dealt. As an application, Heisenberg type uncertainty principle for Clifford shearlet transform has been derived.

中文翻译：

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Clifford值Shearlet变换

本文讨论了使用小波群\（（\ mathbb {R} ^ ）构造\（n = 3 \ text {mod} 4 \） Clifford代数\（Cl_ {n，0} \）值可容许小波变换的构造。 * <imes \ mathbb {R} ^ {n-1}）<imes \ mathbb {R} ^ n \）是\（{\ mathbb {R}} ^ n \）的仿射组的子组。获得了非零Clifford值平方可积函数的可容许条件。处理了诸如重建公式，正交关系，等轴测图和再现内核的各种属性。作为一种应用，推导了用于Clifford剪切波变换的Heisenberg型不确定性原理。