English

On functions of bounded variation

Classical Analysis and ODEs 2016-06-13 v2 Functional Analysis Numerical Analysis

Abstract

The recently introduced concept of D\mathcal{D}-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from Pausinger \& Svane (J. Complexity, 2014) whether every function of bounded Hardy--Krause variation is Borel measurable and has bounded D\mathcal{D}-variation. Moreover, we show that the space of functions of bounded D\mathcal{D}-variation can be turned into a commutative Banach algebra.

Keywords

Cite

@article{arxiv.1510.04522,
  title  = {On functions of bounded variation},
  author = {Christoph Aistleitner and Florian Pausinger and Anne Marie Svane and Robert F. Tichy},
  journal= {arXiv preprint arXiv:1510.04522},
  year   = {2016}
}
R2 v1 2026-06-22T11:21:14.676Z