Some Generalizations of the Notion of Bounded Variation

Some Generalizations of the Notion of Bounded Variation

Functions of bounded variation were first introduced in 1881 by Camille Jordan, who was seeking a sufficient condition for a function f to have a Fourier series that sums to f [5]. Pierce and Velleman discuss several equivalent definitions and some generalizations of the notion of bounded variation.

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Veröffentlicht in:The American mathematical monthly 2006-12, Vol.113 (10), p.897-904
Hauptverfasser: Pierce, Pamela B., Velleman, Daniel J.
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Closed intervals
Continuous functions
Fourier analysis
Fourier series
Mathematical functions
Mathematical intervals
Mathematical sequences
Mathematical theorems
Mathematics
Series convergence
Theorems
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Beschreibung
Zusammenfassung:Functions of bounded variation were first introduced in 1881 by Camille Jordan, who was seeking a sufficient condition for a function f to have a Fourier series that sums to f [5]. Pierce and Velleman discuss several equivalent definitions and some generalizations of the notion of bounded variation.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2006.11920377