Constructive approach to the monotone rearrangement of functions

Giovanni Barbarino, Davide Bianchi, Carlo Garoni*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We detail a simple procedure (easily convertible to an algorithm) for constructing, from quasi-uniform samples of f, a sequence of linear spline functions converging to the monotone rearrangement of f, in the case where f is an almost everywhere continuous function defined on a bounded set Ω with negligible boundary. Under additional assumptions on f and Ω, we prove that the convergence of the sequence is uniform. We also show that the same procedure applies to arbitrary measurable functions too, but with the substantial difference that in this case the procedure has only a theoretical interest and cannot be converted to an algorithm.

Original languageEnglish
JournalExpositiones Mathematicae
DOIs
Publication statusE-pub ahead of print - 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Almost everywhere continuous functions
  • Asymptotically uniform grids and quasi-uniform samples
  • Generalized inverse distribution function
  • Monotone rearrangement
  • Quantile function
  • Uniform convergence

Fingerprint

Dive into the research topics of 'Constructive approach to the monotone rearrangement of functions'. Together they form a unique fingerprint.

Cite this