All reports by Author Naomi Kirshner:

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TR19-130
| 26th September 2019
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Naomi Kirshner, Alex Samorodnitsky#### A moment ratio bound for polynomials and some extremal properties of Krawchouk polynomials and Hamming spheres

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TR18-016
| 25th January 2018
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Naomi Kirshner, Alex Samorodnitsky#### On $\ell_4$ : $\ell_2$ ratio of functions with restricted Fourier support

Revisions: 1

Naomi Kirshner, Alex Samorodnitsky

Let $p \ge 2$. We improve the bound $\frac{\|f\|_p}{\|f\|_2} \le (p-1)^{s/2}$ for a polynomial $f$ of degree $s$ on the boolean cube $\{0,1\}^n$, which comes from hypercontractivity, replacing the right hand side of this inequality by an explicit bivariate function of $p$ and $s$, which is smaller than $(p-1)^{s/2}$ for ... more >>>

Naomi Kirshner, Alex Samorodnitsky

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 >>>