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Electronic Colloquium on Computational Complexity

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Reports tagged with Uncertainty principle:
TR12-031 | 4th April 2012
Tom Gur, Omer Tamuz

Testing Booleanity and the Uncertainty Principle

Revisions: 1

Let $f:\{-1,1\}^n \to \mathbb{R}$ be a real function on the hypercube, given
by its discrete Fourier expansion, or, equivalently, represented as
a multilinear polynomial. We say that it is Boolean if its image is
in $\{-1,1\}$.

We show that every function on the hypercube with a ... more >>>

TR18-016 | 25th January 2018
Naomi Kirshner, Alex Samorodnitsky

On $\ell_4$ : $\ell_2$ ratio of functions with restricted Fourier support

Revisions: 1

Given a subset $A\subseteq \{0,1\}^n$, let $\mu(A)$ be the maximal ratio between $\ell_4$ and $\ell_2$ norms of a function whose Fourier support is a subset of $A$. We make some simple observations about the connections between $\mu(A)$ and the additive properties of $A$ on one hand, and between $\mu(A)$ and ... more >>>

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