# A Caracterization of N-dimensional Daubechies Type Tensor by Dengfeng L., Silong P. PDF

By Dengfeng L., Silong P.

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Example text

19. 2006 For m = 0, this would be the Coulomb-Potential, but like this, it’s called the Yukawa-Potential. m usually means the mass of a particle. We want to do the Fourier Transform. We first check R3 e−m|x| dx = |x| = ∞ 2π π 0 e−mr sin θ r 2 dθ dφ dr r 0 0 ∞ 2π = = = sin θ dθ 0 0 = π e−mr 2 r dr r −4π d dm ∞ e−mr dr 0 d e−mr −4π dm −m d 1 −4π dm m 4π m−2 ∞ 0 So, this function is in L1 (R3 ) and we can do the Fourier Transform. For this, we know k, x = Rk, Rx ∀R ∈ O(3), k, x ∈ R3 and for each k ∈ R3 , there is an R ∈ SO(3), such that Rk = (0, 0, |k|).

52 N Newtonian gravitational field . . . 1 O orthogonal algebra . . . . . . .

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