Discrepancy and numerical integration on metric measure spaces

Luca Brandolini, William W. L. Chen, Leonardo Colzani, Giacomo Gigante*, Giancarlo Travaglini

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)
    3 Downloads (Pure)

    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 Lp discrepancy with respect to certain classes of subsets, for example, metric balls.

    Original languageEnglish
    Pages (from-to)328-369
    Number of pages42
    JournalJournal of Geometric Analysis
    Volume29
    Issue number1
    DOIs
    Publication statusPublished - Jan 2019

    Keywords

    • Discrepancy
    • Numerical integration
    • Metric measure spaces

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