On the Clifford-Fourier transform

2010/03/02 by Hendrik De Bie, Yuan Xu, De Bie, H. +1
Mathematics · #30G35 #42B10 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1003.0689

openalex publication_date 2010/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For functions that take values in the Clifford algebra, we study the Clifford-Fourier transform on R^m defined with a kernel function K(x,y) := e^(i π)/(2) Γ_ye^-i , replacing the kernel eⁱ of the ordinary Fourier transform, where Γ_y := - ∑_j

Citations

• Conformally invariant powers of the ambient Dirac operator

Related

• The kernel of the generalized Clifford-Fourier transform and its generating function
• A new construction of the Clifford-Fourier kernel
• The class of Clifford-Fourier transforms
• The fractional Clifford-Fourier transform
• On the radially deformed Fourier transform