Octonion Beurling theorem: uncertainty principles for Hermite functions on \(\mathbb{R}^3\)

DOI10.1002/mma.9811zbMath1547.42018MaRDI QIDQ6551526

Shihao Fan, Guang Bin Ren

Publication date: 7 June 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

Fourier transformsuncertainty principlesoctonionBeurling theorem

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Measures of information, entropy (94A17)

Cites Work

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• The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer
• 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.
• Beurling's theorem for the quaternion Fourier transform
• A generalization of the octonion Fourier transform to 3-D octonion-valued signals: properties and possible applications to 3-D LTI partial differential systems
• Quaternion Fourier transform on quaternion fields and generalizations
• Information theoretic inequalities
• The octonions
• Dynamical versions of Hardy’s uncertainty principle: A survey
• Beurling's theorem in the Clifford algebras
• Beurling's theorem associated with octonion algebra valued signals

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