Discrepancy and numerical integration on metric measure spaces
Analysis of PDEs
2018-02-19 v3 Numerical Analysis
Number Theory
Abstract
We study here the error of numerical integration on metric measure spaces adapted to a decomposition of the space into disjoint subsets. We consider both the error for a single given function, and the worst case error for all functions in a given class of potentials. The main tools are the classical Marcinkiewicz-Zygmund inequality and ad hoc definitions of function spaces on metric measure spaces. The same techniques are used to prove the existence of point distributions in metric measure spaces with small discrepancy with respect to certain classes of subsets, for example metric balls.
Cite
@article{arxiv.1308.6775,
title = {Discrepancy and numerical integration on metric measure spaces},
author = {Luca Brandolini and William W. L. Chen and Leonardo Colzani and Giacomo Gigante and Giancarlo Travaglini},
journal= {arXiv preprint arXiv:1308.6775},
year = {2018}
}