Abstract
It is of main interest in the theory and also in applications of Fourier series that how to reconstruct a function from the partial sums of its Walsh-Fourier series. In 1955 Fine proved the Fejer-Lebesgue theorem, that is for each integrable function we have the almost everywhere convergence of Fejer means σn f→f. It is also of prior interest that what can be said - with respect to this reconstruction issue - if we have only a subsequence of the partial sums. In this paper we give a brief resume of the recent results with respect to this issue above also regarding the class of two-variable integrable functions.
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