Some new thin sets of integers in Harmonic ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Some new thin sets of integers in Harmonic Analysis
Author(s) :
Li, Daniel [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Queffélec, Hervé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rodriguez-Piazza, Luis [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Queffélec, Hervé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rodriguez-Piazza, Luis [Auteur]
Journal title :
Journal d'analyse mathématique
Pages :
105-138
Publisher :
Springer
Publication date :
2002
ISSN :
0021-7670
English keyword(s) :
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.
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.
HAL domain(s) :
Mathématiques [math]/Analyse fonctionnelle [math.FA]
English abstract : [en]
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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
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