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Clifford Wavelet Transform and the Uncertainty Principle

A Correction to this article was published on 14 October 2020

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Abstract

The present paper lies in the whole topic of wavelet harmonic analysis on Clifford algebras. In which we derive a Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, wavelet transform on \(\mathbb {R}\) and Clifford Fourier transform and their properties is conducted. Next, such concepts are applied to develop an uncertainty principle based on Clifford wavelets.

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  • 14 October 2020

    Unfortunately, there is the slight error in the affiliation of Dr. H. Banouh.

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Correspondence to Anouar Ben Mabrouk.

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Banouh, H., Ben Mabrouk, A. & Kesri, M. Clifford Wavelet Transform and the Uncertainty Principle. Adv. Appl. Clifford Algebras 29, 106 (2019). https://doi.org/10.1007/s00006-019-1026-4

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  • DOI: https://doi.org/10.1007/s00006-019-1026-4

Keywords

  • Harmonic analysis
  • Clifford algebra
  • Clifford analysis
  • Continuous wavelet transform
  • Clifford Fourier transform
  • Clifford wavelet transform
  • Uncertainty principle

Mathematics Subject Classification

  • 30G35
  • 42C40
  • 42B10
  • 15A66