The structure of regulated functions
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- by Casper Goffman, Gadi Moran and Daniel Waterman PDF
- Proc. Amer. Math. Soc. 57 (1976), 61-65 Request permission
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
- J. Musielak and W. Orlicz, On generalized variations. I, Studia Math. 18 (1959), 11–41. MR 104771, DOI 10.4064/sm-18-1-11-41
- S. Perlman, Functions of generalized variation, Fund. Math. 105 (1979/80), no. 3, 199–211. MR 580582, DOI 10.4064/fm-105-3-199-211
- Daniel Waterman, On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107–117. MR 310525, DOI 10.4064/sm-44-2-107-117
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 61-65
- MSC: Primary 26A45
- DOI: https://doi.org/10.1090/S0002-9939-1976-0401993-5
- MathSciNet review: 0401993