6 papers
Almost positive kernels on compact Riemannian manifolds
Bianca Gariboldi, Giacomo Gigante
We show how to build a kernel \[ K_X(x,y)=\sum_{m=0}^Xh(λ_m/{λ_X})φ_m(x)\overline{φ_m(y)} \] on a compact Riemannian manifold , which is positive up to a negligible error and su…
On a sharp lemma of Cassels and Montgomery on manifolds
Luca Brandolini, Bianca Gariboldi, Giacomo Gigante
Let be a -dimensional compact connected Riemannian manifold and let be a complete sequence of orthonormal…
Discrepancy of a convex set with zero curvature at one point
Bianca Gariboldi
Let be a convex body with everywhere positive curvature except at the origin and with the boundary as the graph of the function in…
Asymptotically optimal cubature formulas on manifolds for prefixed weights
Martin Ehler, Ujué Etayo, Bianca Gariboldi +2
We propose a new extension of the proof of the Korevaar-Meyers conjecture by Bondarenko, Radchenko and Viazovska for cubature formulas with prefixed weights (we fix different weigh…
Variance of Lattice Point Counting in Thin Annuli
Leonardo Colzani, Bianca Gariboldi, Giacomo Gigante
We give asymptotic estimates of the variance of the number of integer points in translated thin annuli in any dimension.
Discrepancy for convex bodies with isolated flat points
Luca Brandolini, Leonardo Colzani, Bianca Gariboldi +2
We consider the discrepancy of the integer lattice with respect to the collection of all translated copies of a dilated convex body having a finite number of flat, possibly non-smo…