The class of Clifford-Fourier transforms

DOI10.1007/s00041-011-9177-2zbMath1237.30017arXiv1101.1793OpenAlexW2073995959MaRDI QIDQ657871

Juan-Miguel Gracia

Publication date: 10 January 2012

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

Full work available at URL: https://arxiv.org/abs/1101.1793

zbMATH Keywords

Fourier transformClifford analysisClifford-Fourier transformBessel-Gegenbauer serieshypercomplex signals

Mathematics Subject Classification ID

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

Related Items

Slice Fourier transform and convolutions ⋮ The bounds of the odd dimensional Clifford-Fourier kernels ⋮ Some properties of the spinor Fourier transform ⋮ A new construction of the Clifford-Fourier kernel ⋮ The fractional Clifford-Fourier transform ⋮ Two-sided fractional Clifford–Fourier transformation ⋮ The Atiyah-Singer index theorem for a family of fractional Dirac operators on spin geometry ⋮ Beurling's theorem for the Clifford‐Fourier transform ⋮ Pseudo‐differential operator in quaternion space ⋮ Uncertainty principles for the Clifford-Fourier transform ⋮ Fourier kernels associated with the Clifford-Helmholtz system ⋮ Lifting of quaternionic frames to higher dimensions with partial ridges ⋮ Clifford algebras, Fourier transforms, and quantum mechanics ⋮ Convolution products for hypercomplex Fourier transforms ⋮ Inequalities in the setting of Clifford analysis ⋮ Closed form of the Fourier-Borel kernel in the framework of Clifford analysis ⋮ Clifford algebra method for network expression, computation, and algorithm construction ⋮ Demystification of the geometric Fourier transforms and resulting convolution theorems ⋮ Spectrums of functions associated to the fractional Clifford-Fourier transform ⋮ On the Clifford short-time Fourier transform and its properties ⋮ Dunkl operators and a family of realizations of $\mathfrak{osp}(1\vert2)$

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