Pointwise strong approximation of almost periodic functions in S^1

Abstract

We consider the Fourier series of S1 almost periodic functions and construct the matrix means of partial sums of such series by the class GM (2β) . In two approximation theorems using these means we give the estimates of pointwise strong deviation of such means from the functions in terms of moduli of continuity defined by the Gabisoniya points, and the best approximation of functions by entire functions. Mathematics subject classification (2010): 42A247.