| http://www.w3.org/ns/prov#value | - It is easy to see that $\hat G$ is locally compact (in the compact open topology) What Fourier analysis becomes in this case is a method for expressing an arbitrary element of $L^2(G)$ as an integral of the form $f(g) \sim \int \hat f(\chi)\chi(g) d\chi$, where $\hat f$, the Fourier transform of $f$ is defined dually by $\hat f(\chi) = \int f(g) \chi(g)
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