Listar Departamento de Matemáticas y Estadística por autor "Shmerkin, Pablo"
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An improved bound for the dimension of (α, 2α)-Furstenberg sets
Shmerkin, Pablo; Héra, Kornélia; Yavicoli, Alexia (2022)We show that given α e (0, 1) there is a constant c = c α > 0 such that any planar (α, 2α)-Furstenberg set has Hausdorff dimension at least 2α + c. This improves several previous bounds, in particular extending a result ... -
Inverse theorems for discretized sums and Lq norms of convolutions in Rd
Shmerkin, Pablo (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
Shmerkin, Pablo; Orponen, Tuomas; De Saxcé, Nicolás (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 ... -
On the volumes of simplices determined by a subset of Rd
Shmerkin, Pablo; Yavicoli, Alexia (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 ...