On functions of bounded variation

Christoph Aistleitner; Florian Pausinger; Anne Marie Svane; Robert Tichy

doi:10.1017/S0305004116000633

On functions of bounded variation

Christoph Aistleitner, Florian Pausinger^*, Anne Marie Svane, Robert Tichy

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

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 [20] 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.

Original language	English
Pages (from-to)	405-418
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	162
Issue number	3
DOIs	https://doi.org/10.1017/S0305004116000633
Publication status	Published - 2017

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Information, Communication & Computing

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Theoretical

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10.1017/S0305004116000633

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title = "On functions of bounded variation",

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 [20] 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.",

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AU - Svane, Anne Marie

AU - Tichy, Robert

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AB - 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 [20] 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.

U2 - 10.1017/S0305004116000633

DO - 10.1017/S0305004116000633

M3 - Article

SN - 1469-8064

VL - 162

SP - 405

EP - 418

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -

On functions of bounded variation

Abstract

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