A new construction of the Clifford-Fourier kernel

DOI10.1007/s00041-016-9476-8zbMath1365.42007arXiv1509.01960OpenAlexW2963770113MaRDI QIDQ2397691

Hendrik De Bie, Denis Constales, Lian Pan

Publication date: 23 May 2017

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.01960

zbMATH Keywords

Laplace transformBessel functionClifford-Fourier transformplane wave decomposition

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Laplace transform (44A10)

Related Items (15)

Approximation properties of the sampling Kantorovich operators: regularization, saturation, inverse results and Favard classes in \(L^p\)-spaces ⋮ The bounds of the odd dimensional Clifford-Fourier kernels ⋮ Two-sided fractional Clifford–Fourier transformation ⋮ Convergence Results for Nonlinear Sampling Kantorovich Operators in Modular Spaces ⋮ Linear prediction and simultaneous approximation by \(m\)-th order Kantorovich type sampling series ⋮ The kernel of the generalized Clifford-Fourier transform and its generating function ⋮ Fourier kernels associated with the Clifford-Helmholtz system ⋮ Inverse results of approximation and the saturation order for the sampling Kantorovich series ⋮ The max-product generalized sampling operators: convergence and quantitative estimates ⋮ Saturation by the Fourier transform method for the sampling Kantorovich series based on bandlimited kernels ⋮ A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods ⋮ Convergence of sampling Kantorovich operators in modular spaces with applications ⋮ On the Clifford short-time Fourier transform and its properties ⋮ Approximation by max-product sampling Kantorovich operators with generalized kernels ⋮ Max-product type multivariate sampling operators and applications to image processing

Cites Work

• The fractional Clifford-Fourier transform
• The fractional Clifford-Fourier kernel
• The class of Clifford-Fourier transforms
• The Clifford-Fourier integral kernel in even dimensional Euclidean space
• The two-dimensional Clifford-Fourier transform
• The Clifford-Fourier transform
• On the Clifford-Fourier Transform
• Harmonic Analysis in Phase Space. (AM-122)
• Generalized Fourier Transforms Arising from the Enveloping Algebras of 𝔰𝔩(2) and 𝔬𝔰𝔭(1∣2)
• Uncertainty principles for integral operators
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