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Let $G$ be a compact abelian group with dual $\Gamma$. Let $\Lambda \subset \Gamma$ a Sidon set (see the book of Rudin: Fourier Analysis on Groups for the definition).

Consider the set $\Lambda\times\Lambda$.

Is it a Sidon set of $\Gamma\times \Gamma$?

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    What is a Sidon set in the context of general compact abelian groups? I am used to Sidon sets being sets of integers.2011-10-25
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    @DJC: These are defined somewhere in Rudin's book on Fourier Analysis - I don't have my copy here right now, but it has to do with continuous functions on $G$ whose Fourier transforms are supported on $\Lambda$.2011-10-26
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    I updated the question. It seems that there exists several notions of "Sidon set".2012-01-25

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