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Sets of multiplicity and differentiable functions


Author: R. Kaufman
Journal: Proc. Amer. Math. Soc. 32 (1972), 472-476
MSC: Primary 42A48; Secondary 43A46
DOI: https://doi.org/10.1090/S0002-9939-1972-0340928-7
MathSciNet review: 0340928
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Abstract: The paper contains two theorems relating the fine structure of differentiable functions, in one or more dimensions, to the behavior of Fourier-Stieltjes transforms on sets that are small in various ways.


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

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  • [2] J.-P. Kahane, Approximation par des exponentielles imaginaires; ensembles de Dirichlet et ensembles de Kronecker, Proc. Conf. Abstract Spaces and Approximation (Oberwolfach, 1968), Birkhauser, Basel, 1969, pp. 190-202. MR 41 #5846. MR 0261230 (41:5846)
  • [3] R. Kaufman, A functional method for linear sets, Israel J. Math 5 (1967), 185-187. MR 38 #4902. MR 0236607 (38:4902)
  • 1. -, II, ibid. 7 (1969), 293-298. MR 41 #7382. MR 0262777 (41:7382)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0340928-7
Keywords: $ {M_0}$-set, Kronecker set, $ {C^1}$ topology
Article copyright: © Copyright 1972 American Mathematical Society

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