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Journal Articles Journal d'analyse mathématique Year : 2002

Some new thin sets of integers in Harmonic Analysis

Daniel Li
Hervé Queffélec
  • Function : Author
  • PersonId : 859618
Luis Rodriguez-Piazza
  • Function : Author
  • PersonId : 859619


We randomly construct various subsets $\Lambda$ of the integers which have both smallness and largeness properties. They are small since they are very close, in various meanings, to Sidon sets: the continuous functions with spectrum in $\Lambda$ have uniformly convergent series, and their Fourier coefficients are in $\ell_p$ for all $p>1$; moreover, all the Lebesgue spaces $L^q_\Lambda$ are equal for $q<+\infty$. On the other hand, they are large in the sense that they are dense in the Bohr group and that the space of the bounded functions with spectrum in $\Lambda$ is non separable. So these sets are very different from the thin sets of integers previously known.
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hal-00442352 , version 1 (21-12-2009)



Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Some new thin sets of integers in Harmonic Analysis. Journal d'analyse mathématique, 2002, 86, pp.105-138. ⟨hal-00442352⟩
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