24 citations · 60 across the 18 of their papers we have counts for
6 papers · 1 filter
Jittered sampling and probability measures
Roberto Bramati, Luca Brandolini, Giancarlo Travaglini
This paper investigates the discrepancy of a family of random sampling methods obtained by perturbing the grid , where …
Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies
Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini
W. Schmidt, H. Montgomery, and J. Beck proved a result on irregularities of distribution with respect to -dimensional balls. In this paper, we extend their result to any -dim…
Convergence of multiple Fourier series and Pick's theorem
Luca Brandolini, Leonardo Colzani, Sinai Robins +1
We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's t…
and Weak- estimates for the number of integer points in translated domains
Luca Brandolini, Leonardo Colzani, Giacomo Gigante +1
Revisiting and extending a recent result of M.Huxley, we estimate the and Weak- norms of the discrepancy be…
Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus
Luca Brandolini, Leonardo Colzani, Giacomo Gigante +1
We produce explicit low-discrepancy infinite sequences which can be used to approximate the integral of a smooth periodic function restricted to a convex domain with positive curva…
Quadrature rules and distribution of points on manifolds
Luca Brandolini, Christine Choirat, Leonardo Colzani +3
We study the error in quadrature rules on a compact manifold. As in the Koksma-Hlawka inequality, we consider a discrepancy of the sampling points and a generalized variation of th…