On functions of bounded variation
Classical Analysis and ODEs
2016-06-13 v2 Functional Analysis
Numerical Analysis
Abstract
The recently introduced concept of -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 -variation. Moreover, we show that the space of functions of bounded -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}
}