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Bounded variation in the mean

Author(s): Pamela B. Pierce; Daniel Waterman
Journal: Proc. Amer. Math. Soc. 128 (2000), 2593-2596.
MSC (1991): Primary 26A45, 42A16, 42A20
Posted: February 21, 2000
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Abstract | References | Similar articles | Additional information

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.

References:

[MS]: Móricz, F., Siddiqi, A. H., A quantified version of the Dirichlet-Jordan test in $L^{1}$ -norm, Rend. Circ. Mat. Palermo (2) 45 (1996), no. 1, 19-24. MR 97k:42009
[W]: Waterman, Daniel, A generalization of the Salem test, Proc. Amer. Math. Soc. 105 (1989), no. 1, 129-133. MR 89e:42007

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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: 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
Posted: February 21, 2000
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 2000, American Mathematical Society


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