Thin sets defined by a sequence of continuous functions. (English) Zbl 1032.42009
The paper studies thin sets of reals defined from a sequence \(\{f_n\}\) of continuous real functions in a similar way as trigonometric thin sets are defined from the sequence \(\{\operatorname {sin} 2 \pi nx\}\). There are also given some conditions under which such families form a trigonometric like family. The paper shows that all important classical results on trigonometric thin sets can be proved in a more general case.
Reviewer: L’ubica Holá (Bratislava)
MSC:
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
| 43A46 | Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) |
| 42C15 | General harmonic expansions, frames |
Keywords:
trigonometric thin set; Borel basis; permitted set; well distributed sequence; Salem theorem; Arbault-Erdős theoremReferences:
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