The Fourier expansion of a boolean function $f : \{-1,1\}^n \to \{-1,1\}$ is simply its representation as a real, multilinear polynomial. (Multilinear means that no variable $x_i$ appears squared, cubed, etc.) For example, suppose $n = 2$ and $f = {\textstyle \min_2}$, the “minimum” function on $2$ bits:

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Ohad Klein: Are the indexing in (the start of) 7 OK?Ohad Klein: "learning algorithm running in time in time"Amir: In the proof of Theorem 16, and in the equation immediately ...Ohad Klein: In example 6, should "of codimension less than n" be "of pos...Ohad Klein: In 15c (18c in the book), I think it should be $\cap_j{V_j}$...Ohad Klein: Bracket typo: In the proof of thm 10 (12 in the book), $sgn(...Ohad Klein: Oops, my bad.