The fact that the Fourier characters $\chi_{\gamma} : {\mathbb F}_2^n \to \{-1,1\}$ form a group isomorphic to ${\mathbb F}_2^n$ is not a coincidence; the analogous result holds for any finite abelian group and is a special case of the theory of Pontryagin duality in harmonic analysis. We will see further examples of this in Chapter [...]

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Ohad Klein: In lemma 46 (48) - should it be $i \not \in J'_x$? (In its ...Ohad Klein: Another one - is the symbol "union" is redundant in 37b,c?Ohad Klein: I might be misunderstanding 37b. Suppose k=n=1. Then $E[f^q]...Ohad Klein: I might be wrong, but in ex. 9.31 (i.e. remark 9.29), I trie...Ohad Klein: sorry, my bad, again!Ohad Klein: In 23, is it $q \leq 2+2\epsilon$?Ohad Klein: ctrl+f: Paresval.