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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bounded variation in the mean


Authors: Pamela B. Pierce and Daniel Waterman
Journal: Proc. Amer. Math. Soc. 128 (2000), 2593-2596
MSC (1991): Primary 26A45, 42A16, 42A20
Published electronically: February 21, 2000
MathSciNet review: 1670415
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Abstract:

It is shown that the concept of bounded variation in the mean is not a meaningful generalization of ordinary bounded variation. In fact, it is a characterization of functions which differ from functions of bounded variation on a zero set.


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Additional Information

Pamela B. Pierce
Affiliation: Department of Mathematical Sciences, The College of Wooster, Wooster, Ohio 44691
Email: ppierce@acs.wooster.edu

Daniel Waterman
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244; Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431
Address at time of publication: 7739 Majestic Palm Dr., Boynton Beach, Florida 33437
Email: fourier@earthlink.net

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05391-0
PII: S 0002-9939(00)05391-0
Keywords: Bounded variation, Fourier series
Received by editor(s): October 7, 1998
Published electronically: February 21, 2000
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society