Generalization of the Abel-Poisson method for summations of Fourier trigonometric series

We also note that the problem studied in this paper was posed when the author reported at the seminar on the theory of functions of a real variable at Moscow State University in April 2013. A partial answer was given by the author in his lecture at the International Conference “Contemporary Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, III” in Rostov-on-Don (Southern Federal University, June 2–6, 2013). © 2014 Pleiades Publishing, Ltd., R. M. Trigub. All rights reserved.