Some remarks on functions of bounded variation
Authors:
S. Perlman and D. Waterman
Journal:
Proc. Amer. Math. Soc. 74 (1979), 113118
MSC:
Primary 26A45
MathSciNet review:
521883
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Abstract: It is shown that if a function has no external saltus, then its total variation is independent of its values at points of discontinuity, and a function which is equal to the given function at points of continuity cannot have a lesser total variation. Necessary and sufficient conditions are determined for one space to contain another and for two spaces to be identical.
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 C. Goffman, Everywhere convergence of Fourier series, Indiana Univ. Math. J. 20 (1970), 107113. MR 0270048 (42:4941)
 [3]
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 [4]
 , A characterization of the class of functions whose Fourier series converge for every change of variable, J. London Math. Soc. (2) 10 (1975), 6974. MR 0370036 (51:6265)
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 , The localization principle for double Fourier series (to appear).
 [6]
 S. Perlman, Functions of generalized variation, Fund. Math. (to appear). MR 580582 (81h:26007)
 [7]
 D. Waterman, On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107117. MR 0310525 (46:9623)
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 , On the summability of Fourier series of functions of bounded variation, Studia Math. 55 (1976), 97109.
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 , On bounded variation, Studia Math. 57 (1976), 3345. MR 0417355 (54:5408)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919790521883X
PII:
S 00029939(1979)0521883X
Article copyright:
© Copyright 1979
American Mathematical Society
