The sizes of the classes of $H^{(N)}$-sets

Volume 226 / 2014

Václav Vlasák Fundamenta Mathematicae 226 (2014), 201-220 MSC: 43A46, 42A63. DOI: 10.4064/fm226-3-1


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.


  • Václav VlasákFaculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic

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