Convolution theorems for quaternion Fourier transform: properties and applications

DOI10.1155/2013/162769zbMath1297.42015OpenAlexW2039603470WikidataQ58915400 ScholiaQ58915400MaRDI QIDQ2016662

Mawardi Bahri, Rémi Vaillancourt, Ryuichi Ashino

Publication date: 20 June 2014

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/162769

zbMATH Keywords

heat equationconvolutionhypoellipticityquaternion algebraquaternion Fourier transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Heat equation (35K05) Hypoelliptic equations (35H10) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Harmonic analysis and PDEs (42B37)

Related Items (10)

A modified uncertainty principle for two-sided quaternion Fourier transform ⋮ A simplified proof of uncertainty principle for quaternion linear canonical transform ⋮ Uncertainty principle for the two sided quaternion windowed Fourier transform ⋮ Beurling's theorem for the quaternion Fourier transform ⋮ Uncertainty principles for the continuous quaternion shearlet transform ⋮ Quaternion offset linear canonical transform in one-dimensional setting ⋮ Uncertainty principle for the two-sided quaternion windowed Fourier transform ⋮ A convolution theorem related to quaternion linear canonical transform ⋮ On Heisenberg and local uncertainty principles for the multivariate continuous quaternion shearlet transform ⋮ Multilinear Localization Operators Associated to Quaternion Fourier Transforms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two-dimensional quaternion wavelet transform
• Clifford Fourier transformation and uncertainty principle for the Clifford geometric algebra \(\mathrm{Cl}_{3,0}\)
• Biquaternion (complexified quaternion) roots of \(- 1\)
• Windowed Fourier transform of two-dimensional quaternionic signals
• Clifford Fourier transform on multivector fields and uncertainty principles for dimensions \(n=2\pmod 4\) and \(n=3\pmod 4\)
• A general geometric Fourier transform convolution theorem
• Local quaternion Fourier transform and color image texture analysis
• Fractional quaternion Fourier transform, convolution and correlation
• An uncertainty principle for quaternion Fourier transform
• Quaternion Fourier transform on quaternion fields and generalizations
• Hypercomplex Fourier Transforms of Color Images
• Image Processing: The Fundamentals
• Directional uncertainty principle for quaternion Fourier transform

This page was built for publication: Convolution theorems for quaternion Fourier transform: properties and applications