Problems in the Approximation of $$2pi $$ -Periodic Functions by Fourier Sums in the Space $$L_2 (2pi )$$

In this paper, using the Steklov function, we introduce the modulus of continuity and define the classes of functions $W_{2,varphi }^{r,k} $ and $W_varphi ^{r,k} $ in the spaces L ₂ and C. For the class $W_{2,varphi }^{r,k} $ , we calculate the order of the Kolmogorov width and, for the class $W_varphi ^{r,k} $ , we obtain an estimate of the error of a quadrature formula.