Some new thin sets of integers in Harmonic Analysis

Li, Daniel ; Queffélec, Hervé ; Rodriguez-Piazza, Luis

HAL, hal-00442352 / Harvested from HAL

Résumé

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.

Détail

Publié le : 2002-07-05
Classification:  uniformly distributed set,  ergodic set,  lacunary set,  $\Lambda(q)$-set,  quasi-independent set,  random set,  $p$-Rider set,  Rosenthal set,  $p$-Sidon set,  set of uniform convergence,  uniformly distributed set.,  MSC: Primary: 42A36 ; 42A44 ; 42A55 ; 42A61 ; 43A46; Secondary: 60D05,  [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]