2019
Том 71
№ 11

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

Konyushkov A. A.

Abstract

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 } such that $a_n ≥ α_n, b_n ≥ Β_n,\; n = 1, 2$.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 10, pp 1636-1643.

Citation Example: Konyushkov A. A. Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series // Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1455–1460.

Full text