Giacomo Gigante

On the Koksma-Hlawka inequality

The classical Koksma Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma Hlawka type inequality which applies to piecewise smooth functions

Quadrature rules and distribution of points on manifolds

f\chi_{\Omega}

A Koksma-Hlawka inequality for simplices

, with

AVERAGE DECAY ESTIMATES FOR FOURIER TRANSFORMS OF MEASURES SUPPORTED ON CURVES

f

Localization for Riesz means of Fourier expansions

smooth and

Optimized Schwarz methods for the diffusion-reaction problem with cylindrical interfaces

\Omega

Analysis and optimization of the generalized Schwarz method for elliptic problems with application to fluid---structure interaction

a Borel subset of

Diameter Bounded Equal Measure Partitions of Ahlfors Regular Metric Measure Spaces

[0,1]^{d}

Lp and Weak–Lp estimates for the number of integer points in translated domains

.

Discrepancy for randomized Riemann sums

We study the error in quadrature rules on a compact manifold. Our estimates are in the same spirit of the Koksma-Hlawka inequality and they depend on a sort of discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.