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Some remarks on functions of $ \Lambda $-bounded variation


Authors: S. Perlman and D. Waterman
Journal: Proc. Amer. Math. Soc. 74 (1979), 113-118
MSC: Primary 26A45
DOI: https://doi.org/10.1090/S0002-9939-1979-0521883-X
MathSciNet review: 521883
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Abstract: It is shown that if a $ \Lambda {\text{BV}}$ function has no external saltus, then its total $ \Lambda $-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 $ \Lambda $-variation. Necessary and sufficient conditions are determined for one $ \Lambda {\text{BV}}$ space to contain another and for two spaces to be identical.


References [Enhancements On Off] (What's this?)

  • [1] A. Baernstein and D. Waterman, Functions whose Fourier series converge uniformly for every change of variable, Indiana Univ. Math. J. 22 (1972), 569-576. MR 0310523 (46:9621)
  • [2] C. Goffman, Everywhere convergence of Fourier series, Indiana Univ. Math. J. 20 (1970), 107-113. MR 0270048 (42:4941)
  • [3] C. Goffman and D. Waterman, Functions whose Fourier series converge for every change of variable, Proc. Amer. Math. Soc. 19 (1968), 80-86. MR 0221193 (36:4245)
  • [4] -, A characterization of the class of functions whose Fourier series converge for every change of variable, J. London Math. Soc. (2) 10 (1975), 69-74. MR 0370036 (51:6265)
  • [5] -, 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), 107-117. MR 0310525 (46:9623)
  • [8] -, On the summability of Fourier series of functions of $ \Lambda $-bounded variation, Studia Math. 55 (1976), 97-109.
  • [9] -, On $ \Lambda $-bounded variation, Studia Math. 57 (1976), 33-45. MR 0417355 (54:5408)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0521883-X
Article copyright: © Copyright 1979 American Mathematical Society

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