Thomas Beretti

activity

20242026

collaborators

3 papers

math.CA2026

Polynomial-order oscillations in geometric discrepancy

Thomas Beretti

Let $C \subset R^{2}$ be a convex body, and for a positive integer $N$ , let $P$ be a configuration of $N$ points in $[0, 1)^{2}$ . The discrepancy of $P$ with…

math.NT2025

The Fourier transform of planar convex bodies and discrepancy over intervals of rotations

Thomas Beretti

This work studies the Fourier transform of the characteristic function of planar convex bodies averaged over affine transformations. We establish lower and upper bounds on the latt…

math.CA2024

Fourier transform of BV functions and applications

Thomas Beretti, Luca Gennaioli

This paper investigates the relation between the Fourier transform of {\rm BV} (bounded variation) functions and their jump sets. We introduce the notion of $L^{2}$ -jump product and…