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On functions of bounded variation†

Published online by Cambridge University Press:  26 July 2016

CHRISTOPH AISTLEITNER ,
FLORIAN PAUSINGER ,
ANNE MARIE SVANE  and
ROBERT F. TICHY
CHRISTOPH AISTLEITNER
Affiliation:
Johannes Kepler University Linz e-mail: aistleitner@math.tugraz.at
FLORIAN PAUSINGER*
Affiliation:
TU Munich e-mail: florian.pausinger@gmx.at
ANNE MARIE SVANE
Affiliation:
Aarhus University e-mail: amsvane@math.au.dk
ROBERT F. TICHY
Affiliation:
TU Graz e-mail: tichy@tugraz.at
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Abstract

The recently introduced concept of ${\mathcal D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from [20] whether every function of bounded Hardy–Krause variation is Borel measurable and has bounded ${\mathcal D}$-variation. Moreover, we show that the space of functions of bounded ${\mathcal D}$-variation can be turned into a commutative Banach algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 3 , May 2017 , pp. 405 - 418
Copyright
Copyright © Cambridge Philosophical Society 2016 

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Footnotes

†

Corresponding author: Florian Pausinger, TU Munich, Zentrum Mathematik, M10 Geometrie und Visualisierung, Boltzmannstr. 3, 85748 Garching.

References

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