An approximation of class of convolutions of periodic functions by linear methods based on their Fourier-Lagrange coefficients

Abstract

We calculate the least upper bounds of pointwise and uniform approximations for classes of $2\pi$-periodic functions expressible as convolutions of an arbitrary square summable kernel with functions, which belong to the unit ball of the space $L_2$, by linear polynomial methods, constructed on the basis of their Fourier-Lagrange coefficients.