Abstract : 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.
https://hal-univ-artois.archives-ouvertes.fr/hal-00442352
Contributor : Daniel Li
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Submitted on : Monday, December 21, 2009 - 8:45:27 AM
Last modification on : Tuesday, July 3, 2018 - 11:34:18 AM
Long-term archiving on : Thursday, June 17, 2010 - 11:58:34 PM
Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Some new thin sets of integers in Harmonic Analysis. Journal d'analyse mathématique, Springer, 2002, 86, pp.105-138. ⟨hal-00442352⟩
