24 citations · 60 across the 18 of their papers we have counts for
7 papers · 1 filter
Discrepancy estimates for multi-dimensional non-smooth convex bodies: a case study
Roberto Bramati, Luca Brandolini, Alessandro Monguzzi
We study -averaged discrepancies of finite sequences of points in the torus with respect to translated and dilated copies of convex bodies with non-smooth bound…
Single radius spherical cap discrepancy on compact two-point homogeneous spaces
Luca Brandolini, Bianca Gariboldi, Giacomo Gigante +1
In this note we study estimates from below of the single radius spherical discrepancy in the setting of compact two-point homogeneous spaces. Namely, given a -dimensional manifo…
On a discrete approach to lower bounds in discrepancy theory
Luca Brandolini, Bianca Gariboldi, Giacomo Gigante +1
In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the…
Irregularities of distribution for bounded sets and half-spaces
Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
An Euler-Maclaurin formula for polygonal sums
Luca Brandolini, Leonardo Colzani, Sinai Robins +1
We prove an Euler-Maclaurin formula for double polygonal sums and, as a corollary, we obtain approximate quadrature formulas for integrals of smooth functions over polygons with in…
Average decay estimates for Fourier transforms of measures supported on curves
Luca Brandolini, Giacomo Gigante, Allan Greenleaf +3
We consider Fourier transforms of densities supported on curves in R^d. We obtain sharp lower and close to sharp upper bounds for the L^q decay rates.