degree-1 « Analysis of Boolean Functions

Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1108#comment-20795" title="On: Chapter 6 exercises">Yes, thanks!
Dmitry Sokolov: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1108#comment-20794" title="On: Chapter 6 exercises">Exercise 28. Maybe $A \in \{-1, 1\}$ istead of $A \in \mathb...
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1545#comment-20625" title="On: §10.2: Hypercontractivity of general random variables">Fixed, thanks!
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1517#comment-20624" title="On: Chapter 10: Advanced hypercontractivity">It's the Holder conjugate of $q$ (i.e., the number satisfyin...
Gautam Kamath: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1517#comment-20003" title="On: Chapter 10: Advanced hypercontractivity">Is $q'$ defined here?
Gautam Kamath: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1545#comment-20002" title="On: §10.2: Hypercontractivity of general random variables">On this page, Hölder is displaying for me as H{ö}lder - is t...
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1665#comment-19238" title="On: §11.1: Gaussian space and the Gaussian noise operator">Yes, you're right. This is not a well-written proof by the ...

§5.4: Degree-1 weight

In this section we prove two theorems about the degree-$1$ Fourier weight of boolean functions: \[ \mathbf{W}^{1}[f] = \sum_{i=1}^n \widehat{f}(i)^2. \]

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Analysis of Boolean Functions

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§5.4: Degree-1 weight

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