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Beurling’s theorem for the quaternion Fourier transform

Abstract

The two-sided quaternion Fourier transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Beurling’s theorem, Hardy, Cowling–Price and Gelfand–Shilov theorems, is obtained for the two-sided quaternion Fourier transform.

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Correspondence to Youssef El Haoui.

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El Haoui, Y., Fahlaoui, S. Beurling’s theorem for the quaternion Fourier transform. J. Pseudo-Differ. Oper. Appl. 11, 187–199 (2020). https://doi.org/10.1007/s11868-019-00281-7

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Keywords

  • Quaternion Fourier transform
  • Beurling’s theorem
  • Uncertainty principles