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arXiv · 0912.4214

Some new thin sets of integers in Harmonic Analysis

Daniel Li·Hervé Queffélec·Luis Rodriguez-Piazza
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Abstract

We randomly construct various subsets $Λ$ 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 $Λ$ have uniformly convergent series, and their Fourier coefficients are in $\ell_p$ for all $p>1$; moreover, all the Lebesgue spaces $L^q_Λ$ 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 $Λ$ is non separable. So these sets are very different from the thin sets of integers previously known.

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Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. 2009-12-21. Some new thin sets of integers in Harmonic Analysis. https://arxiv.org/abs/0912.4214

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