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Proving the conjecture of O’Donnell in certain cases and disproving its general validity
For a function $f:\\{−1,1\\}^n\\to \\{−1,1\\}$ the relationship between the sum of its linear Fourier coefficients $\\hat{f}(i)$ (defined by $\\hat{f}(i)≔\\frac{1}{2^n}\\sum_{x\in \\{−1,1\\}^n} f(x)x_i$ for $i=1,2,\\ldots,n$ and …
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