Questions tagged [poisson-summation-formula]

For questions dealing with the Poisson Summation Formula

The Poisson Summation Formula expresses a relation between the Fourier Series Coefficients of a periodic function and the values of its Fourier Transform given by

$$\sum_{n=-\infty}^\infty f(x+n)~=~\sum_{k=-\infty}^\infty e^{2\pi i kx}\int_{-\infty}^\infty f(t)e^{-2\pi ikt}\mathrm dt$$

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Poisson Summation Formula with vector functions

I want to derive the form of the Poisson Summation Formula as in Equation (6) of this this paper which is $$ \frac{1}{L^3} \sum_{\vec{k}} g(\vec{k}) = \int \frac{d^3 k}{(2\pi)^3} g(\vec{k}) + \sum_{\vec{l} \neq \vec{0} } \int \frac{d^3 k}{(2\pi)^3}…