I ran into this Fourier transform: $\int_{ \mathbb{R} ^n}e^{-\pi \sum_{k=1}^{n}u_i \mid c^k_1 x_1+c_2^k x_2...+c^k_n x_n \mid^2}e^{-2\pi i(m_1x_1+m_2x_2...+m_n x_n))}dx_1dx_2...dx_n$ ($c^k_a$ is the ath constant in a set k, not $(c_a)^k$, and $u_i$ is a constant) I thought about substituting the equation in the absolute value sign with another variable so that I could separate the sum in the exponent, but I don't know how to deal with the differential under that substitution. I believe there is a way to solve this, but I don't know how. If someone could show me I'd appreciate the help.
2026-03-30 05:11:09.1774847469
N-dimensional Fourier transform
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