Beurling's theorem for the quaternion Fourier transform

DOI10.1007/S11868-019-00281-7zbMath1475.42018arXiv1711.04142OpenAlexW3104280871WikidataQ128353341 ScholiaQ128353341MaRDI QIDQ2174855

Youssef El Haoui, Saïd Fahlaoui

Publication date: 27 April 2020

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.04142

zbMATH Keywords

uncertainty principlesBeurling's theoremquaternion Fourier transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (13)

Uncertainty principles for the two-sided quaternion linear canonical transform ⋮ Boundedness and uniqueness of quaternion Weyl transform ⋮ Generalized uncertainty principles associated with the quaternionic offset linear canonical transform ⋮ Uncertainty principles for Wigner-Ville distribution associated with the quaternion offset linear canonical transform ⋮ The Beurling theorem in space-time algebras ⋮ Uncertainty principles for the fractional quaternion Fourier transform ⋮ Beurling's theorem in the Clifford algebras ⋮ Beurling's theorem associated with octonion algebra valued signals ⋮ Tighter Heisenberg-Weyl type uncertainty principle associated with quaternion wavelet transform ⋮ The 2-D hyper-complex Gabor quadratic-phase Fourier transform and uncertainty principles ⋮ Inequalities Pertaining to Quaternion Ambiguity Function ⋮ On uncertainty principle for the two-sided quaternion linear canonical transform ⋮ A new uncertainty principle related to the generalized quaternion Fourier transform

Cites Work

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• Pitt's inequality and the uncertainty principle associated with the quaternion Fourier transform
• A uniqueness theorem of Beurling for Fourier transform pairs
• The uncertainty principle: A mathematical survey
• Hermite functions and uncertainty principles for the Fourier and the windowed Fourier trans\-forms.
• The uncertainty principle for the two-sided quaternion Fourier transform
• Convolution theorems for quaternion Fourier transform: properties and applications
• Quaternion Fourier transform on quaternion fields and generalizations
• Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT

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