ON THE RECOVERY OF THE COEFFICIENTS OF A REARRANGED HAAR SERIES

Abstract

The author has previously established that, for any rearrangement of a Haar series, if the rearranged series converges everywhere on to a bounded function then the coefficients of the series can be recovered from the sum using the formulas of Fourier; however, no analogous assertion holds, in general, for an arbitrary summable function .Generalizing his previous results, the author shows, in particular, that the theorem on the recovery of the coefficients of a rearranged Haar series goes over to functions of the class , but not to the class for any .Bibliography: 9 titles.