Thin sets of integers in Harmonic analysis and p-stable random Fourier series.

Pascal Lefèvre (1) , Daniel Li (1) , Hervé Queffélec (2) , Luis Rodriguez-Piazza (3)

1 LML - Laboratoire de Mathématiques de Lens
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 departamento analisis matematico

We investigate the behavior of some thin sets of integers defined through random trigonometric polynomial when one replaces Gaussian or Rademacher variables by p-stable ones, with 1 < p < 2. We show that in one case this behavior is essentially the same as in the Gaussian case, whereas in another case, this behavior is entirely different.

Mots clés: Fourier series; quasi-independent set; Rider set; stable random variables; stationary set; stationary set.

Domaines: Analyse fonctionnelle [math.FA]

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Thin sets of integers in Harmonic analysis and p-stable random Fourier series.. 2009. ⟨hal-00361386⟩