Approximation by linear methods of classes of $(\psi,\bar\beta)-$differentiable functions.

Abstract

We calculate the least upper bounds for approximations in the metric of the space $L_2$ by linear methods of summation of Fourier series on classes of periodic functions $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers $\psi=\psi(k)$ and shifts of argument $\bar\beta=\beta_k$