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Measures on independent sets, a quantitative version of Rudin's theorem


Author: T. W. Körner
Journal: Proc. Amer. Math. Soc. 135 (2007), 3823-3832
MSC (2000): Primary 42A16
DOI: https://doi.org/10.1090/S0002-9939-07-09095-8
Published electronically: August 23, 2007
MathSciNet review: 2341932
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Abstract: We construct measures with independent support whose Fourier coefficients decrease as fast as possible.


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

  • 1. F. Hausdorff, Set theory. Second edition. Translated from the German by John R. Aumann et al., Chelsea Publishing Co., New York, 1957. MR 0086020 (19:111a)
  • 2. J. P. Kahane, Images d'ensembles parfaits par des séries de Fourier gaussienes C. R. Acad. Sci. Paris Sér. A-B 263 (1966) A678-A681.
  • 3. J. P. Kahane, Some random series of functions. Second edition. Cambridge Studies in Advanced Mathematics, 5. Cambridge University Press, Cambridge, 1985. MR 833073 (87m:60119)
  • 4. J. P. Kahane and R. Salem, Ensembles parfaits et séries trigonométriques. Herman, Paris, 1963. MR 0160065 (28:3279)
  • 5. R. Kaufman, A functional method for linear sets Israel J. Math. 5 (1967) 185-7. MR 0236607 (38:4902)
  • 6. R. Kaufman, Measures in independent sets Studia Math. 30 (1968) 17-20. MR 0227698 (37:3282)
  • 7. R. Kaufman, Small subsets of finite Abelian groups Annales de l'Institut Fourier 18 (1968) 99-102. MR 0241532 (39:2872)
  • 8. T. W. Körner A topological Ivašev-Musatov theorem J. London Math. Soc. (2) 67 (2003), 448-460 MR 1956146 (2004b:42006)
  • 9. W. Rudin Fourier-Stieltjes transforms of measures on independent sets Bull. Amer. Math. Soc. 66 (1960) 199-202. MR 0119035 (22:9802)
  • 10. R. Salem, On singular monotonic functions whose spectrum has a given Hausdorff dimension Ark. Mat. 1 (1951) 353-365. MR 0043249 (13:230b)

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Additional Information

T. W. Körner
Affiliation: DPMMS, Centre for Mathematical Sciences, Clarkson Road, Cambridge, England
Email: twk@dpmms.cam.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-07-09095-8
Keywords: Rudin set, independent set, Fourier series
Received by editor(s): March 16, 2006
Published electronically: August 23, 2007
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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