On behavior of Fourier coefficients by Walsh system

摘要

The paper proves that for any epsilon > 0 there exists ameasurable set E aS, [0, 1] with measure |E| > 1 - epsilon such that for each f a L-1[0, 1] there is a function coinciding with f on E whose Fourier-Walsh series converges to in L (1)[0, 1]-norm, and the sequence is monotonically decreasing, where is the sequence of Fourier-Walsh coefficients of (f) over tilde .