Clifford Valued Shearlet Transform

Abstract

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.

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Acknowledgements

The authors would like to express their sincere gratitude to the referees for their insightful and valuable comments and suggestions.

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Correspondence to Shivam Kumar Singh.

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Communicated by Eckhard Hitzer

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Sharma, J., Singh, S.K. Clifford Valued Shearlet Transform. Adv. Appl. Clifford Algebras 30, 38 (2020). https://doi.org/10.1007/s00006-020-01066-8

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Keywords

  • Clifford Fourier transform
  • Clifford shearlet transform
  • shearlet group
  • uncertainty principle

Mathematics Subject Classification

  • Primary 42C40
  • 15A66
  • Secondary 94A12