The sizes of the classes of $H^{(N)}$-sets
Fundamenta Mathematicae, Tome 226 (2014) no. 3, pp. 201-220
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
The class of $H^{(N)}$-sets forms an important subclass of the class of sets of uniqueness for trigonometric series. We investigate the size of this class which is reflected by the family of measures (called polar) annihilating all sets from the class. The main aim of this paper is to answer in the negative a question stated by Lyons, whether the polars of the classes of $H^{(N)}$-sets are the same for all $N\in \mathbb {N}$. To prove our result we also present a new description of $H^{(N)}$-sets.
Keywords:
class sets forms important subclass class sets uniqueness trigonometric series investigate size class which reflected family measures called polar annihilating sets class main paper answer negative question stated lyons whether polars classes sets mathbb prove result present description sets
Affiliations des auteurs :
Václav Vlasák 1
@article{10_4064_fm226_3_1,
author = {V\'aclav Vlas\'ak},
title = {The sizes of the classes of $H^{(N)}$-sets},
journal = {Fundamenta Mathematicae},
pages = {201--220},
publisher = {mathdoc},
volume = {226},
number = {3},
year = {2014},
doi = {10.4064/fm226-3-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm226-3-1/}
}
Václav Vlasák. The sizes of the classes of $H^{(N)}$-sets. Fundamenta Mathematicae, Tome 226 (2014) no. 3, pp. 201-220. doi: 10.4064/fm226-3-1
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