On the Salem test of the uniform convergence of the trigonometric Fourier series

Author: Teimuraz Akhobadze
Keywords: Fourier series, uniform convergence, Salem test
Annotation:

The assertion that the Salem test for the uniform convergence of a trigonometric Fourier series is improvable, is proved. In particular, an example of a continuous function, which does not fulfill the condition of the Salem test but satisfies the condition of the generalized Salem test is constructed.