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Mediterranean Journal of Mathematics

, Volume 9, Issue 2, pp 403–407 | Cite as

Some Supports of Fourier Transforms of Singular Measures are not Rajchman

  • Maria Roginskaya
Article
  • 53 Downloads

Abstract

The notion of Riesz sets tells us that a support of Fourier transform of a measure with non-trivial singular part has to be large. The notion of Rajchman sets tells us that if the Fourier transform tends to zero at infinity outside a small set, then it tends to zero even on the small set. Here we present a new angle of an old question: Whether every Rajchman set should be Riesz.

Mathematics Subject Classification (2010)

Primary 42A16 Secondary 43A05 

Keywords

Rajchman sets Riesz sets Riesz products singular measures support of Fourier transform 

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References

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    Rajchman A.: Une classe de series trigonometriques. Math. Ann. 101, 686–700 (1929)MathSciNetMATHCrossRefGoogle Scholar
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    F. Riesz, M. Riesz, Über Rantwerte einer analytischen Funktionen. Quatrième Congrès des Math. Scand. Stockholm (1916), pp. 27–44Google Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Mathematical SciencesChalmers University of TechnologyGothenburgSweden
  2. 2.Mathematical SciencesGothenburg UniversityGothenburgSweden

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