hypercontractivity « Analysis of Boolean Functions

Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1315#comment-12047" title="On: §8.2: Generalized Fourier formulas ">Thanks Albert, keep them coming!
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1323#comment-12046" title="On: §8.3: Orthogonal decomposition">Thanks!
Albert Atserias: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1323#comment-11996" title="On: §8.3: Orthogonal decomposition">In equation (4), $\phi(\alpha)$ should be $\phi_{\alpha}$.
Albert Atserias: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1315#comment-11984" title="On: §8.2: Generalized Fourier formulas ">Hi Ryan. Typo: In the proof of Proposition 19, in the expect...
Deepak: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1339#comment-11901" title="On: §8.4: $p$-biased analysis">Cool! That all makes sense.
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1189#comment-11893" title="On: §7.2: Probabilistically checkable proofs of proximity">Thanks on both!
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1339#comment-11892" title="On: §8.4: $p$-biased analysis">1. Fixed, thanks 2. Fixed, thanks 3. For the first two occ...

Chapter 1 notes

The Fourier expansion for real-valued boolean functions dates back to Walsh [Wal23] who introduced a complete orthonormal basis for $L^2([0,1])$ consisting of $\pm 1$-valued functions, constant on dyadic intervals.

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Analysis of Boolean Functions

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