Abstract:
Series with respect to a system of characters of a zero-dimensional compact commutative group are considered. Generalization of the test of convergence of Fourier series of the Vilenkin system in the case of unbounded quasimonotone $p_k$ for functions having a generalized bounded $\Phi$-fluctuation, which was earlier obtained in the case of bounded sequences $p_k$, is proved.
Key words:zero-dimensional group, characters of a group, Fourier series, Salem test, Vilenkin system.
Fulltext:
PDF file (315 kB)