degree-1 « Analysis of Boolean Functions

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 ...
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1694#comment-19237" title="On: §11.2: Hermite polynomials">Thanks, yes.
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1694#comment-19236" title="On: §11.2: Hermite polynomials">Yep, thanks.
Ryan O'Donnell: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1612#comment-19235" title="On: Chapter 10 exercises">Yep, thanks.
Noam Lifshitz: <a href="http://www.contrib.andrew.cmu.edu/~ryanod/?p=1612#comment-19148" title="On: Chapter 10 exercises">I think that in exercise 23, it should be $(p,2)$ Hypercontr...

§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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