Approximation by linear methods of summation of orthogonal series

We give an estimate of the rapidity of convergence of certain linear means of the orthogonal series _k =0 c_{k k} (x) to the functionf (x) L₂ (a, b) defined by this series according to the Riesz-Fisher theorem for almost all x (a, b). The results obtained are, in a certain sense, final.Translated from Matematicheskie Zametki, Vol. 3, No. 3, pp. 345–356, March, 1968.