Absolute summability of orthogonal series by Euler’s method

We have obtained a sufficient condition for the absolute summability of an orthogonal series by the (E, 1) method. We have proved that if the coefficients of the orthogonal series decrease monotonically in absolute value, then the condition we have found is exact. We have shown that for coefficients decreasing not necessarily monotonically the condition given is not exact. Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 51–56, January, 1977.