The class of -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 -sets are the same for all N ∈ ℕ. To prove our result we also present a new description of -sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-3-1,
author = {V\'aclav Vlas\'ak},
title = {The sizes of the classes of $H^{(N)}$-sets},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {201-220},
zbl = {1301.43006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-3-1}
}
Václav Vlasák. The sizes of the classes of $H^{(N)}$-sets. Fundamenta Mathematicae, Tome 227 (2014) pp. 201-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-3-1/