Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series

• Date: 1993
• Main Authors: Konyushkov, A. A., Конюшков, А. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5951
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study restrictions that should be imposed on the numbers sequences $\{α_n\}$ and $\{Β_n\}$ in order to guarantee that the series $\sum\nolimits_{n = 1}^\infty {a_n } \cos nx$ and $\sum\nolimits_{n = 1}^\infty {b_n } \sin nx$ do not belong to the classes $B$ or $C$ for any {a n } and {b n }...