[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that the Pontrjagin dual of [math]\mathbb Z_N[/math] is this group itself

[[math]] \widehat{\mathbb Z}_N=\mathbb Z_N [[/math]]

and work out the details of the subsequent isomorphism [math]C^*(\mathbb Z_N)\simeq C(\mathbb Z_N)[/math].