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Proceedings of the American Mathematical Society

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The structure of regulated functions


Authors: Casper Goffman, Gadi Moran and Daniel Waterman
Journal: Proc. Amer. Math. Soc. 57 (1976), 61-65
MSC: Primary 26A45
MathSciNet review: 0401993
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Abstract: It is shown that there is a nontrivial class of regulated functions each of which is a representable as the sum of a continuous function and a uniformly convergent series of jump functions whose jumps are those of the given function. The set of regulated functions is the union of the classes of functions of bounded $ \Phi $-variation for convex $ \Phi $.


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

  • [1] J. Musielak and W. Orlicz, On generalized variations. I, Studia Math. 18 (1959), 11–41. MR 0104771
  • [2] S. Perlman, Functions of generalized variation, Fund. Math. 105 (1979/80), no. 3, 199–211. MR 580582
  • [3] Daniel Waterman, On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107–117. Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity. II. MR 0310525

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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0401993-5
Article copyright: © Copyright 1976 American Mathematical Society