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 | References | Similar Articles | Additional Information
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.
- [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 236607, https://doi.org/10.1007/BF02771106
- 1. R. Kaufman, A functional method for linear sets. II, Israel J. Math. 7 (1969), 293–298. MR 262777, https://doi.org/10.1007/BF02788861
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1972-0340928-7
Keywords:
-set,
Kronecker set,
topology
Article copyright:
© Copyright 1972
American Mathematical Society
