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

• Autorzy: Václav Vlasák
• Języki publikacji: EN

Abstrakty

EN

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 ∈ ℕ. To prove our result we also present a new description of $H^{(N)}$-sets.

Kategorie tematyczne

• 42A63: Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 226
• Numer: 3
• Strony: 201-220

Daty

wydano

2014

Twórcy

autor

Václav Vlasák

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

Identyfikatory

DOI

10.4064/fm226-3-1