Some new thin sets of integers in Harmonic ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Some new thin sets of integers in Harmonic Analysis
Auteur(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]
Titre de la revue :
Journal d'analyse mathématique
Pagination :
105-138
Éditeur :
Springer
Date de publication :
2002
ISSN :
0021-7670
Mot(s)-clé(s) en anglais :
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.
Discipline(s) HAL :
Mathématiques [math]/Analyse fonctionnelle [math.FA]
Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Collections :
Source :
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