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On the n−th linear polarization constant of Rn
(Mathematische Nachrichten, 2023)
Abstract. We prove that given any set of n unit vectors {vi}n
i=1 ⊂ Rn, the
inequality
sup
kxkRn=1
|hx, v1i · · · hx, vni| ≥ n−n/2
holds for n ≤ 14. Moreover, the equality is attained if and only if {vi}n
i=1 is
an ...
Inverse theorems for discretized sums and Lq norms of convolutions in Rd
(Universidad Torcuato Di Tella, 2023)
We prove inverse theorems for the size of sumsets and the L
q norms of
convolutions in the discretized setting, extending to arbitrary dimension an earlier
result of the author in the line. These results have applications ...
On the Fourier decay of multiplicative convolutions
(Universidad Torcuato Di Tella, 2023)
We prove the following. Let $\mu_{1},\ldots,\mu_{n}$ be Borel probability measures on $[-1,1]$ such that $\mu_{j}$ has finite $s_j$-energy for certain indices $s_{j} \in (0,1]$ with $s_{1} + \ldots + s_{n}>1$. Then, the ...