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Analysis Mathematica

, Volume 44, Issue 3, pp 381–387 | Cite as

On the Zero Sets of the Fourier Transform of Singular Measures

  • M. WojciechowskiEmail author
Article
  • 38 Downloads

Abstract

We show that the class of sets E with the property that there exists a measure singular with respect to the Lebesgue measure whose Fourier transform tends to 0 at infinity and vanishes on E contains the Helson sets.

Key words and phrases

singular measure special set 

Mathematics Subject Classification

42A38 

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References

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    P. Matilla, Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press (1995).CrossRefGoogle Scholar
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    M. Roginskaya and M. Wojciechowski, On a summability of measures with thin spectra, Ann. Inst. Fourier (Grenoble), 54 (2004), 413–430.MathSciNetCrossRefzbMATHGoogle Scholar
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    A. Zygmund, Trigonometric Series, Cambridge University Press (1959).zbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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