Distributional Formulation
These equations can be interpreted in the language of distributions (Córdoba 1988; Hörmander 1983, §7.2) for a function or distribution, whose derivatives are all rapidly decreasing (see Schwartz function). Using the Dirac comb distribution and its Fourier series:
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(Eq.5)
Eq.1 readily follows:
Similarly:
Read more about this topic: Poisson Summation Formula
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