Abstract
We apply the results on the integral approximation of the characteristic function of an interval by the subspace \( \mathcal{T}_{n - 1} \) of trigonometric polynomials of order at most n − 1, which were obtained by the authors earlier, to investigate the Jackson inequality between the best uniform approximation of a continuous periodic function by the subspace \( \mathcal{T}_{n - 1} \) and its modulus of continuity of the second order. The corresponding method of the uniform approximation of continuous periodic functions by trigonometric polynomials is constructed.
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