Pablo Shmerkin

activity

20042025

most citedLocal entropy averages and projections of fractal measures

92 citations · 502 across the 56 of their papers we have counts for

collaborators

Showing 2023Show all

4 papers · 1 filter

math.CA2023

On the volumes of simplices determined by a subset of $R^{d}$

Pablo Shmerkin, Alexia Yavicoli

We prove that for $1 \leq k < d$ , if $E$ is a Borel subset of $R^{d}$ of Hausdorff dimension strictly larger than $k$ , the set of $(k + 1)$ -volumes determined by $k + 2$ points in $…

math.CA2023

On the Fourier decay of multiplicative convolutions

Tuomas Orponen, Nicolas de Saxcé, Pablo Shmerkin

We prove the following. Let $μ_{1}, \dots, μ_{n}$ be Borel probability measures on $[- 1, 1]$ such that $μ_{j}$ has finite $s_{j}$ -energy for certain indices $s_{j} \in (0, 1]$ with $s_{…

math.CA2023★ 1 cited

Inverse theorems for discretized sums and $L^{q}$ norms of convolutions in $R^{d}$

Pablo Shmerkin

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 i…

math.CA2023★ 2 cited

Projections, Furstenberg sets, and the $A B C$ sum-product problem

Tuomas Orponen, Pablo Shmerkin

We make progress on two interrelated problems at the intersection of geometric measure theory, additive combinatorics and harmonic analysis: the discretised sum-product problem, an…

On the volumes of simplices determined by a subset of Rd

On the Fourier decay of multiplicative convolutions

Inverse theorems for discretized sums and Lq norms of convolutions in Rd

Projections, Furstenberg sets, and the ABC sum-product problem

On the volumes of simplices determined by a subset of $R^{d}$

Inverse theorems for discretized sums and $L^{q}$ norms of convolutions in $R^{d}$

Projections, Furstenberg sets, and the $A B C$ sum-product problem