On exact estimates of the convergence rate of fourier series for functions of one variable in the space L (2)[-pi, pi]

摘要

The work is devoted to exact estimates of the convergence rate of Fourier series in the trigonometric system in the space of square summable 2 pi-periodic functions with the Euclidean norm on certain classes of functions characterized by the generalized modulus of continuity. Some N-widths of these classes are calculated, and the residual term of one quadrature formula over equally spaced nodes for a definite integral connected with the issues under consideration is found.