Timeline for How does one use the Poisson summation formula?
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| Jun 26, 2010 at 21:18 | comment | added | KConrad | That "more general principle that Poisson summation exemplifies" is Poisson summation when G is finite. For a function f:G-->C, define its H-average and H-cutoff to be functions on G given by Avg_H(f)(g) = (1/#H)\sum_{h \in H} f(gh) and Cut_H(f)(g) = [f(g) when g is in H and 0 when g is not in H]. Then by a direct calculation, the Fourier transform of the function Avg_H(f) on G is the function Cut_{H^\perp}(f^) on G^, and if you take the Fourier transform of both sides to get an identity of functions on G you get the Poisson summation formula (Here f^(chi) = \sum_{g in G} f(g)chi*(g).) | |
| Jun 21, 2010 at 4:25 | history | edited | Terry Tao | CC BY-SA 2.5 |
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| Jun 21, 2010 at 4:18 | history | answered | Terry Tao | CC BY-SA 2.5 |