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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Sets of multiplicity and differentiable functions


Author: R. Kaufman
Journal: Proc. Amer. Math. Soc. 32 (1972), 472-476
MSC: Primary 42A48; Secondary 43A46
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?)

  • [1] J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708
  • [2] Jean-Pierre Kahane, Approximation par des exponentielles imaginaires; ensembles de Dirichlet et ensembles de Kronecker, Abstract Spaces and Approximation (Proc. Conf., Oberwolfach, 1968) Birkhäuser, Basel, 1969, pp. 190–202 (French). MR 0261230
  • [3] R. Kaufman, A functional method for linear sets, Israel J. Math. 5 (1967), 185–187. MR 0236607
  • 1. R. Kaufman, A functional method for linear sets. II, Israel J. Math. 7 (1969), 293–298. MR 0262777

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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