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On the volumes of simplices determined by a subset of Rd
(Universidad Torcuato Di Tella, 2023)
We prove that for 1 ≤ k < d, if E is a Borel subset of Rd of Hausdorff
dimension strictly larger than k, the set of (k+1)-volumes determined by k+2 points
in E has positive one-dimensional Lebesgue measure. In the case ...
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 ...