Rogosinsky–Bernstein Polynomial Method of Summation of Trigonometric Fourier Series.

General Rogosinsky–Bernstein linear polynomial means of Fourier series are introduced and three convergence criteria as are obtained: for convergence in the space of continuous periodic functions and for convergence almost everywhere with two guaranteed sets (Lebesgue points and -points). For smooth functions, the rate of convergence in norm of , as well as of their interpolation analogues, is also studied. For approximation of functions in , the asymptotics is found along with the rate of decrease of the remainder term. [ABSTRACT FROM AUTHOR]