On the Clifford-Fourier Transform

  title={On the Clifford-Fourier Transform},
  author={Hendrik De Bie and Yuan Xu},
For functions that take values in the Clifford algebra, we study the Clifford–Fourier transform on Rm defined with a kernel function K(x, y) := e iπ 2 Γy e−i〈x,y〉, replacing the kernel ei〈x,y〉 of the ordinary Fourier transform, where Γy := − ∑ j<k ejek(yj∂yk − yk∂yj ). An explicit formula of K(x, y) is derived, which can be further simplified to a finite sum of Bessel functions when m is even. The closed formula of the kernel allows us to study the Clifford–Fourier transform and prove the… CONTINUE READING

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