Donoho-Stark's uncertainty principles in real Clifford algebras

DOI10.1007/s00006-019-1015-7zbMath1428.43004arXiv1902.08465OpenAlexW3105765873WikidataQ127185125 ScholiaQ127185125MaRDI QIDQ2010540

Youssef El Haoui, Saïd Fahlaoui

Publication date: 27 November 2019

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.08465

zbMATH Keywords

uncertainty principleClifford algebrasClifford-Fourier transformDonoho-Stark's uncertainty principle

Mathematics Subject Classification ID

Clifford algebras, spinors (15A66) Other transforms and operators of Fourier type (43A32)

Related Items (18)

Generalization of Titchmarsh's theorems for the Minkowski algebra ⋮ Two-sided fractional Clifford–Fourier transformation ⋮ Abilov's estimates for the Clifford-Fourier transform in real Clifford algebras analysis ⋮ Fractional Fourier transform for space-time algebra-valued functions ⋮ Clifford valued shearlet transform ⋮ Beurling's theorem in the Clifford algebras ⋮ Real Paley-Wiener theorems for the space-time Fourier transform ⋮ Benedicks-Amrein-Berthier type theorem and local uncertainty principles in Clifford algebras ⋮ Modulus of smoothness and approximation theorems in Clifford analysis ⋮ On the fractional space-time Fourier transforms ⋮ Two-sided Fourier transform in Clifford analysis and its application ⋮ Fractional Clifford-Fourier transform and its application ⋮ Heisenberg's and Hardy's uncertainty principles for special relativistic space-time Fourier transformation ⋮ A sharp Clifford wavelet Heisenberg-type uncertainty principle ⋮ Titchmarsh's theorem in Clifford analysis ⋮ Clifford wavelet transform and the uncertainty principle ⋮ Uncertainty principle for space-time algebra-valued functions ⋮ Two-sided fractional quaternion Fourier transform and its application

Cites Work

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• Pitt's inequality and the uncertainty principle associated with the quaternion Fourier transform
• Clifford Fourier transformation and uncertainty principle for the Clifford geometric algebra \(\mathrm{Cl}_{3,0}\)
• \(L^{p}\) Donoho-Stark uncertainty principles for the Dunkl transform on \(\mathbb{R}^{\text{d}}\)
• Clifford Fourier transform on multivector fields and uncertainty principles for dimensions \(n=2\pmod 4\) and \(n=3\pmod 4\)
• Uncertainty principle for the quaternion Fourier transform
• The Clifford-Fourier transform
• Uncertainty Principles and Signal Recovery
• Introduction to nonlinear dispersive equations

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