Pointwise strong approximation of almost periodic functions in S^1
We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of S^1 almost periodic functions from matrix means of partial sums of their Fourier series.
Points of strong summability of Fourier series
In this paper we present a new solution of Hardy and Littlewood's problem concerning strong summability of Fourier series; we also present a property of points of strong summability.
A new class of numerical sequences and its applications to sine and cosine series
First, it is proved that the class of classical quasi-monotone sequences is not comparable to the newly defined class of sequences of ‘rest bounded variation’. Considering this result, we prove three sample theorems for sequences of rest bounded variation, being analogues of the theorems proved earlier for monotone or quasi-monotone sequences. One of them gives a partial answer to a question raised by R. P. Boas Jr.