On exact estimates of the convergence rate of fourier series for functions of one variable in the space L 2[-π, π]
Abstract
The work is devoted to exact estimates of the convergence rate of Fourier series in the trigonometric system in the space of square summable 2π-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.
- Publication:
-
Computational Mathematics and Mathematical Physics
- Pub Date:
- May 2016
- DOI:
- 10.1134/S0965542516050092
- Bibcode:
- 2016CMMPh..56..717K
- Keywords:
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- Fourier series for functions of one variable;
- best approximation of functions;
- generalized modulus of continuity;
- widths of classes of functions;
- quadrature formula over equally spaced nodes for a definite integral;
- exact estimates of the convergence rate of Fourier series